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  • Articles  (18,108)
  • Springer  (18,108)
  • 1970-1974  (18,108)
  • Mathematics  (18,108)
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  • Articles  (18,108)
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  • 1
    Electronic Resource
    Electronic Resource
    Information Processing in the Visual Systems of Arthropods (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 339-340 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461333
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  • 2
    Electronic Resource
    Electronic Resource
    Optimality in the control of environmental systems (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 341-345 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For an environmental system described by a system of nonlinear first-order differential equations, the problem of achieving specified terminal conditions in a given time with a minimum expenditure of resources is considered. The initial conditions and the minimum value are found numerically in a particular example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464612
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  • 3
    Electronic Resource
    Electronic Resource
    Kinetic approach to neural systems: I (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 535-544 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A kinetic model of neural systems is introduced and discussed with statistical mechanics techniques. It is assumed that, for a macroscopic description of the model, it suffices to consider only the distribution for the velocity and position of the impulses, and the distribution for the excitation and position of the neurons, at any timet. Making use of Boltzmann's method for the study of a dilute gas, coupled differential equations for the rate of change with time of the distributions have been constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463265
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  • 4
    Electronic Resource
    Electronic Resource
    Flow of a newtonian fluid through a permeable tube: The application to the proximal renal tubule (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 457-476 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Creeping flow of a Newtonian fluid through a rigid permeable tube is considered and the transmural seepage is assumed to obey Darcy's law. Closed-form solutions for the pressure and velocity fields are presented and equations describing the axial variation of the mean cross-sectional pressure, the axial volumetric flow and the transmural fluid flux are derived. Approximate solutions for small seepage rates are given and are applied to the flow in the proximal renal tubule. Probable values for the epithelium permeability and the intraluminal hydrostatic pressure drop are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463260
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  • 5
    Electronic Resource
    Electronic Resource
    On knowledge and unpleasantness (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 605-605 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463273
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  • 6
    Electronic Resource
    Electronic Resource
    The Kerner linearization method (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 67-76 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We examine in detail Edward Kerner’s method for linearizing the equations of enzyme kinetics. Our main result is the determination of canonical forms for systems which can be linearized by the method. This is done both in general and in the special cases of two and three dimensions where complete results are obtained. The practical problem of identifying linearizable systems is also considered and computable necessary criteria are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461192
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  • 7
    Electronic Resource
    Electronic Resource
    Continuous determination of the volume of a space in a non steady state condition (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 59-66 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general method for determination of the volume of a space in a non steady state condition, in case diffusion might be significant, is developed. Instantaneous mixing of indicators with native fluid is assumed in this first stage of investigation. Theoretical expressions are obtained for the volume of the space and the diffusion coefficient as a function of time. An analysis of feasibility of the method is also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461191
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  • 8
    Electronic Resource
    Electronic Resource
    Passive transfer of low-molecular nonelectrolytes across deformable semi-permeable membranes—II: Dynamics of a single muscle fiber swelling and shrinking and related changes of theT-system tubule form (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 379-401 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of transfer of low-molecular nonelectrolytes across deformable semipermeable membranes of large curvature developed in Part I (Rubinstein, 1974) is used to describe the dynamics of swelling and shrinking of a muscle fiber at the influx and efflux of low-molecular nonelectrolytes. A large set of computations showed that the theory explains the experiments described in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464616
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  • 9
    Electronic Resource
    Electronic Resource
    Heat transfer in perfused biological tissue—I: General theory (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 403-415 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Green's function for heat and matter transport is calculated for an infinite medium in which a convection field v(r,t) makes a contribution to the total heat and matter current. It is given by a uniformly and absolutely convergent series in which every term is calculated from the preceding one merely by integration. The solution procedure is interpreted physically and illustrated by a simple problem in which v(r,t)=const. in space and time. Since the solution contains no intrinsic spatial symmetry, it can serve as a starting point for a theory of heat and mass transport in perfused biological tissue.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464617
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  • 10
    Electronic Resource
    Electronic Resource
    A long wavelength solution for a microorganism swimming in a channel (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 435-444 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The hydrodynamics of a microorganism swimming in a channel is investigated. The microorganism is modeled as a two-dimensional sheet swimming at low Reynolds numbers between two rigid walls. The wavelengths of the propulsive waves passing down the sheet are assummed to be very large compared to the channel spacing, but the amplitude of the propulsive waves is arbitrary. Explicit analytical solutions for the propulsive velocity and the rate of energy dissipated in terms of the wave amplitude, channel spacing, wave number, and wave speeds are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464619
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  • 11
    Electronic Resource
    Electronic Resource
    Mathematical models of conception and birth (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 455-456 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464621
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  • 12
    Electronic Resource
    Electronic Resource
    Why are there so many species? (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 477-488 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown from the statistical-mechanical overview of Volterra's ecological model how to reckon the fluctuations of collective variables such as the total population of a genus: and that these fluctuations are much decreased (or that the collective populationsteadiness is enhanced) as the speciation is increased. (A niching of species in time, or phase-niching, is entailed here.) Secondly, it is shown how Preston's log-normal distribution describing the species-abundance relationship, as well as a generalization of such distributions, come forth simply and naturally from the statistical-Volterra-dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463261
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  • 13
    Electronic Resource
    Electronic Resource
    The epileptic neuron: II (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 1-16 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Conditions under which a neuron can maintain repetitive discharges are studied with the view that some light may be shed on the problem of epilepsy. It is shown that if there are excitatory and inhibitory substances as well as binding substances in volved, then for repetitive discharges to occur, the formation of the substances must be intracellular. The geometric physical characteristics of the system are also determining factors. The role of a fatigue factor is considered in an attempt to understand the frequency and duration of mild and severe epileptic attacks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461186
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  • 14
    Electronic Resource
    Electronic Resource
    On the number of phenotype structures in genetic systems (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 325-338 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Phenotype structures in genetic systems are carefully defined in an abstract setting so that a considerable amount of enumerative theory can be brought to bear on the problem of enumerating them. Recent results can be used to simplify the computations, and a natural correspondence is suggested which changes the problem of finding the number of phenotype structures to the problem of determining the numbers of certain graphs with colored points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461332
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  • 15
    Electronic Resource
    Electronic Resource
    The interaction of diffusion and perfusion in homogeneous tissue (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 505-526 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463263
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  • 16
    Electronic Resource
    Electronic Resource
    Necessary and sufficient condition for a model insect population to go to extinction (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 527-533 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A necessary and sufficient condition on the parameters for a model population to become extinct is presented. The mathematical model describes an insect population with overlapping generations where the females are polyandrous and the males are subject to autosterilization. The relationship between the values of the parameters of the model and the time to extinction is illustrated.
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    URL: http://dx.doi.org/10.1007/BF02463264
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  • 17
    Electronic Resource
    Electronic Resource
    D'Arcy Thompson's theorems and the shape of the molluscan shell (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 567-575 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper deals with properties of mathematical models of biological systems. It is shown that under suitable conditions the number of parameters employed in the model depends only on the biological system and not on the particular model chosen. As an application the mathematical description of the formation of molluscan shells is discussed.
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    URL: http://dx.doi.org/10.1007/BF02463268
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  • 18
    Electronic Resource
    Electronic Resource
    Molecular control systems: I—Temporal organization in cells revisited (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 595-599 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analysis of Goodwin's fundamental nonlinear oscillator in the light of the requirement that concentrations must be intrinsically non-negative reveals that most of the phase plane is “forbidden”, and that there is one distinguished closed curve that has some of the properties of a limit cycle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463271
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  • 19
    Electronic Resource
    Electronic Resource
    Note on oscillations of turbidity in a precipitation reaction system of thyroxine (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 601-604 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for a precipitation reaction system is presented in which all steps are reversible monomolecular or bimolecular reactions. Under certain conditions, quasi-stable oscillations in turbidity can occur, as has been observed in the precipitation of thyroxine.
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    URL: http://dx.doi.org/10.1007/BF02463272
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  • 20
    Electronic Resource
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    Stabilité structurelle et morphogénèse (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 611-613 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02463275
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  • 21
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    Stochastic processes and applications in biology and medicine. Part 1—Theory. Part 2—Models (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 607-610 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02463274
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  • 22
    Electronic Resource
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    A note on open linear systems (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 97-99 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theorem is given which states a necessary and sufficient condition for the specific activity to be uniform throughout an open compartmental system in the steady state.
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    URL: http://dx.doi.org/10.1007/BF02461195
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  • 23
    Electronic Resource
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    Introduction to Mathematics for Life Scientists (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 101-102 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02461196
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  • 24
    Electronic Resource
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    A dynamic model of an environmental system withn interacting components andp degrees of freedom (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 91-96 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The nonlinear differential equations of growth proposed by Volterra (1931) are used as the basis for a dynamic model of ann-element system withp specified, terminal conditions andp missing initial conditions. The resulting two-point boundary-value problem can be solved, ifp is not large, by the shooting method used previously by Huddleston (1967). A numerical example withn=4 andp=2 is solved on a digital computer, and some results are presented.
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  • 25
    Electronic Resource
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    Use of a heat transfer analogy for a mathematical model of respiratory tract deposition (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 105-116 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mathematical models predicting the aerosol deposition in the respiratory tract are reviewed. Data in the literature indicated not only that the air flow in the trachea and major bronchi may not be laminar, but also that the entrance effect of the tube or airway has not been considered. A new approach to a mathematical model of respiratory tract deposition, based on the analogy of the heat and mass transfer, is discussed.
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    URL: http://dx.doi.org/10.1007/BF02458596
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  • 26
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    Isotherms forr species adsorbed at linear polymers with nearest neighbor cooperative interaction (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 117-126 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The equation of the cooperative specific isotherm is derived for the general case ofr species interacting cooperatively at nearest neighboring sites. Explicit expressions for the special casesr=2–5 are given.
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    URL: http://dx.doi.org/10.1007/BF02458597
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  • 27
    Electronic Resource
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    Pseudo-sound generation at atherosclerotic constrictions in arteries (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 143-155 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Sounds and murmurs have long been employed to qualitatively diagnose cardiovascular disease. However, quantitative diagnosis has been hindered by the lack of understanding of the sound generation and transmission mechanisms. Clinical phonoangiographic studies have shown that simple assumptions about low frequency sound transmission through tissue surrounding an artery are inadequate for obtaining meaningful quantitative diagnosis. Therefore, a theory is developed which relates internal turbulent flow in constricted peripheral arteries to the sound observed at the surface of the skin by means of assumptions of similarity and local axial homogeneity of the internal turbulence. It is found that the spectrum of pressure at the wall of the artery is related to the spectrum of the pressure at the surface of the skin by a filtering factor approximately proportional to ω-2. This arises not because of frequency dependent volumetric absorption in the surrounding medium, as with ultrasound, but because of the manner in which stochastic signals add when observed.
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    URL: http://dx.doi.org/10.1007/BF02458599
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  • 28
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    Measuring a mitotic oscillator: The ARC discontinuity (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 171-182 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mitosis occurs synchronously in up to 108 nuclei in the syncytial plasmodium ofPhysarum polycephalum. Any two phases of the mitotic cycle may be mixed by fusing plasmodial pairs. A topological property of the synchronized phase of the fused pair as a function of parental phases, the arc discontinuity, characterizes the underlying oscillator, and indicates mitosis is controlled by a moderate relaxation oscillator which rotates more rapidly near its singularity than its limit cycle. A model oscillator is briefly described.
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  • 29
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    Genetic nets and dissipative structures: An algebraic approach (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 183-196 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Genetic nets represent an attempt to model genome structure. Depending on the interaction dynamics assumed, they can constitute highly non-linear chemical systems having multiple steady states; hence their relevance to the theory of dissipative structures. Their typical size and possible complexity makes it difficult to study them by means of customary analytical techniques based on differential equations. We have therefore considered an algebraic approach derived from regarding the nets as finite-state automata. This view has revealed a surprisingly rich algebraic structure which can be used to investigate problems concerned with the relation between biological structure and function. This algebraic structure is described with particular reference to the genetic nets of Tsanev and Sendov.
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  • 30
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    Finite fluctuations and multiple steady states far from equilibrium (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 205-213 
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    Notes: Abstract The role of finite fluctuations in transitions between nonequilibrium steady states in nonlinear systems is investigated. Attention is focused on a model biochemical system for which the usual deterministic chemical kinetics predicts a far-from-equilibrium region of multiple steady states. A stochastic approach to chemical kinetics is adopted to study explicitly the effect of fluctuations around the coexisting stable states on a predicted hysteresis in the transition between those states. A numerical solution of the stochastic master equation for the system yields results which differ qualitatively from predictions of the purely macroscopic theory. Possible implications of these results are considered, and several important aspects of the computational scheme are discussed in some detail.
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    URL: http://dx.doi.org/10.1007/BF02458604
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  • 31
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    The global asymptotic stability of prey-predator systems with second-order dissipation (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 215-217 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Models of biological development, evolution and control should take into account that very small numbers of cells or chemicals or individuals eventually grow into stable, large populations. The simplified two-component model used in these studies includes the following: (1) first-order decay; (2) first-order autocatalysis; (3) negative feedback; (4) positive feedback; (5) second-order decay; (6) second-order autocatalysis. A positive definite Lyapunov function is constructed and shown to have a negative definite total derivative. The stationary statex〉0,y〉0, therefore possesses global asymptotic stability. This means that sustained oscillations cannot occur. Another stationary state,x=y=0, is shown to be unstable. This means that infinitesimally small perturbations ofx=y=0 will result in evolution of the variables to the stable stationary state. This result contrasts with that obtained with the Lotka-Volterra model in that small perturbations ofx=y=0 for that model result in sustained, oscillating excursions; the smaller the initial perturbations, the larger these excursions will be. A simulation illustrates that stable populations of 1020 x's andy's can arise from a singlex andy.x grows more or less continuously, buty remains extremely small for 80 per cent of the time interval required for the variables to approach their stable populations.
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  • 32
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    Semiconductor theory of ion transport in thin lipid membranes: II. Surface recombination (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 247-264 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Following the theory of surface recombination in semiconductors, we have derived an expression for the rate of ion recombination at the membrane surface. The surface recombination rate is used in the boundary conditions of current flows at the interfaces. Expressions for the ion fluxes are then derived as functions of environmental variables and membrane parameters. Our analysis strongly suggests that the ion flow through a thin lipid membrane consists of two major components: the surface barrier jumping current and the surface recombination current that are controlled decisively by surface barrier height, surface trap density and surface recombination rates. These general formulations are useful not only for the calculation but also for the understanding of ion transport in thin lipid membranes under a variety of experimental conditions. The implications of this theory to biological membranes and its possible extensions are discussed.
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    URL: http://dx.doi.org/10.1007/BF02461327
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  • 33
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    Transport of O2 along a model pathway through the respiratory region of the lung (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 275-303 
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    ISSN: 1522-9602
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    Notes: Abstract A pathway through the system of branching in the respiratory region of the lung is modelled by a circular cylinder, closed at one end, with partitions which define the component respiratory units. In this model the transport of O2 during inspiration, generated by diffusion is compared with that produced by diffusion together with convection and the importance of convection in the respiratory region in promoting oxygen uptake at the alveolar wall is discussed. For this discussion it is only necessary to consider inspiration. The equations are solved numerically for flow rates of 10, 85 and 200 liters/min. O2 uptake at the wall and curves of constant O2 concentration are shown to illustrate the influence of convection. It is found that after a 2 sec inspiration from an O2 tension of 98 mm Hg and a lung volume of 2300 ml, convection is about 12 per cent as important as diffusion at a flow rate of 85 liters/min, whereas at 10 liters/min convection is only about 0.4 per cent as important as diffusion.
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    Theoretical relationship between the optimal models of the vascular tree (1974)
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    Bulletin of mathematical biology 36 (1974), S. 311-323 
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    Notes: Abstract Two models of optimal branching structure of the vascular tree are compared. Murray’s minimum work model derived from minimum energy loss due to flow and volume in the duct system is proved to be included as a mathematical group in the authors’ model defined by the minimum volume under determinant pressure, flow and position at the terminals. The problem about heterotypical trees which are identical at the terminal conditions but different in the topological order of branch combinations are discussed, applying the results of analyses on the equivalent duct of uniform terminal pressure trees. It is proved that the minimum work tree has the least energy loss compared with its heterotypical minimum volume trees and is a better model of branching structure of the vascular tree.
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    On the stochastic theory of compartments: Solution forn-compartment systems with irreversible, time-dependent transition probabilities (1974)
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    Bulletin of mathematical biology 36 (1974), S. 489-504 
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    Notes: Abstract The bivariate distribution of a two-compartment stochastic system with irreversible, time-dependent transition probabilities is obtained for any point in time. The mean and variance of the number of particles in any compartment and the covariance between the number of particles in each of the two compartments are exhibited and compared to existing results. The two-compartment system is then generalized to ann-compartment catenary and to ann-compartment mammillary system. The multivariate distributions of these two systems are obtained under two sets of initial conditions: (1) the initial distribution is known; and (2) the number of particles in each compartment of the system at timet=0 is determined. The moments of these distributions are also produced and compared with existing results.
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    Dustbathing as a regulatory mechanism (1974)
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    Bulletin of mathematical biology 36 (1974), S. 545-553 
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    Notes: Abstract Three mathematical models were developed to describe how some species of birds, such as bobwhite quail (Colinus virginianus) regulate the amount of oil on their plumage. The models assume that dustbathing plays a significant role in this regulatory process. They differed primarily in their assumptions about the relationship between oiling and dustbathing behavior. Several experiments were run to check on the implications of the models.
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    Observations on the hydrodynamics and swimming motions of mammalian spermatozoa (1974)
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    Bulletin of mathematical biology 36 (1974), S. 555-565 
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    Notes: Abstract An asymptotic solution of the Stokes Flow equations for a self-propelling filament is presented. An explicit expression for the propulsive velocity is obtained for the case of an infinite filament undergoing small amplitude sinusoidal motions. The asymptotic solution is then used to obtain drag coefficients to be used in a simpler approximate analysis which can be applied to experimentally observed motions.
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    Stochastic theory of compartments: One and two compartment systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 577-587 
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    Notes: Abstract Previous work on compartmental systems is generalized (i) to allow the particles present at time zero to have a different lifetime distribution than those which arrive after time zero, and (ii) to allow a particle which enters the system at timet to have a lifetime distribution which is a function oft but is otherwise quite general. The one and two compartment models are analyzed under the above conditions and compared to previous results of Thakuret al. (1974), Purdue (1974) and Cardenas and Matis (1974). Finally, some results for the two compartment, reversible system are given. The analysis used is a blend of direct random variable and queueing theoretic techniques.
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    Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain (1974)
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    Bulletin of mathematical biology 36 (1974), S. 589-593 
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    Notes: Abstract Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d3 x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇2θ+fθ-gθ n+1 , whereD(〉0),n(〉0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f〈0 andg〈0. These results provide general preservation and extinction criteria for the total particle number.
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    Passive transfer of low-molecular nonelectrolytes across deformable semipermeable membranes—I: Equations of convective-diffusion transfer of nonelectrolytes across deformable membranes of large curvature (1974)
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    Bulletin of mathematical biology 36 (1974), S. 365-377 
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    Notes: Abstract The passive transfer of a low-molecular nonelectrolytes mixture across a semipermeable deformable membrane of large curvature is considered. The equations obtained here make it possible to describe the concentration of species redistribution and the change of the membrane shape.
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    A new model for interacting populations—II: Principle of competitive exclusion (1974)
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    Bulletin of mathematical biology 36 (1974), S. 355-364 
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    Notes: Abstract The principle of competitive exclusion is investigated within the framework of the solvable model proposed earlier for two-species systems. The results elucidate the recent controversy over the interpretation of experimental data onDrosophila equilibrium. It is shown that the necessary and sufficient conditions for stable coexistence of competing species is that the product of intraspecific rate constants be greater than the product of interspecific rate constants. Inequalities between rate constants for the occurrence of stable equilibriumbelow andabove the line joining single species equilibria are derived. The availability of larger domain of coexistence suggests that the model presented here has the potential to accommodate a wider class of phenomena than the Gause—Volterra model according to which coexistence is possible only above the line of single species equilibrium.
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    Théorie chromosimique de l'inbreeding: Modèle probabiliste (1974)
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    Bulletin of mathematical biology 36 (1974), S. 417-434 
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    Notes: Abstract A molecular theory of inbreeding involving interactions between zones of gametic recognition (ZRG) localized on the chromosomal sets of male and female gametes is developed. This theory accounts for inbreeding effects and heterosis and raises the problem of control of embryonic development and the biological validity of the inbreeding coefficient. The mathematical analysis of this interaction system with sib matings permits the estimation of viability depression in inbred organisms. The biological validity of the model is discussed.
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    On the probability of reaching a threshold in a stochastic mammillary system (1974)
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    Bulletin of mathematical biology 36 (1974), S. 445-454 
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    Notes: Abstract The multivariate distribution over time of a particular stochastic mammillary compartmental model is obtained for any point in time. The maximum expectation of the peripheral compartments is then derived and used to determine lower bounds on the probability that the maximum of the peripheral compartments reaches any arbitrary threshold level. A bound on the probability is illustrated by an example and some of its implications are explored.
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    Dynamics of populations ofBiomphalaria glabrata and the von forerster equation (1974)
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    Bulletin of mathematical biology 36 (1974), S. 29-37 
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    Notes: Abstract Changes in time of populations ofBiomphalaria glabrata due to changes in the rate of infection bySchistosoma mansomi are investigated. This is done by applying Von Foerster equations with boundary conditions derived from experiment. The resulting equation is solved in some simplified cases and applications of the formalism to ecological problems is suggested.
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    Electrically induced phase transitions via the dipole model in excitable membranes (1974)
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    Bulletin of mathematical biology 36 (1974), S. 17-28 
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    Notes: Abstract Calculations based upon the membrane dipole model have been carried out and indicate the possibility of cooperative behavior during the membrane excitation process. An explicit expression is obtained for the critical electric field,E, which must be present to initiate the cooperative structural transition assumed to occur during membrane excitation. An hypothesis concerning the occurrence of two distinct phase transitions in the membrane resulting in the rapid influx of sodium ions and sodium ion inactivation, respectively, is presented.
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    A note on the shape of the erythrocyte (1974)
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    Bulletin of mathematical biology 36 (1974), S. 55-58 
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    Notes: Abstract Variational calculus is used to derive an equation for the shape of the cross section of a human red blood cell, the objective being the maximization of the surface area/volume ratio. Comparison to previous work is presented.
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    An intergral method for the analysis of flow in arterial stenoses (1974)
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    Bulletin of mathematical biology 36 (1974), S. 39-53 
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    Notes: Abstract An approximate solution is presented to the problem of incompressible flow through an axisymmetric constriction. The geometry is intended to simulate an arterial stenosis, and the solution is applicable to both mild and severe stenoses for Reynolds numbers below transition. Theoretical results obtained for specific geometries are given for the velocity distribution, pressure drop, wall shearing stress, and separation phenomena. These results reveal the significant alterations in flow caused by a stenosis. Experiments using model stenoses are described and compared with the theoretical results. Theoretical predictions of pressure drop and separation characteristics are in reasonably good agreement with the experimental observations.
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    Matematicheskie problemy v biologii (1974)
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    Bulletin of mathematical biology 36 (1974), S. 615-616 
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    The University of Texas Health Science Center at Houston, Division of Continuing Education and The Region V of IEEE announces Eleventh Symposium on Biomathematics and Computer Science in the Life Sciences (1974)
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    Bulletin of mathematical biology 36 (1974), S. 617-617 
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    The simulation of multi-neurone networks: Modelling of the lateral inhibition of the eye and the generation of respiratory rhythm (1974)
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    Bulletin of mathematical biology 36 (1974), S. 77-89 
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    Notes: Abstract We describe a model of a single neurone, and a method of interconnecting such neurone models suitable for multi-neurone network simulations on a digital computer. Two simulations are described; the lateral inhibition in the eye of the Limulus and the generation of respiratory rhythm in the brain stem of the cat.
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    Pulse velocities in cylindrical, tapered and curved anisotropic elastic arteries (1974)
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    Bulletin of mathematical biology 36 (1974), S. 103-103 
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    Interaction of peristaltic motion with Poiseuille flow (1974)
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    Bulletin of mathematical biology 36 (1974), S. 127-141 
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    Notes: Abstract The effect of Poiseuille flow on peristaltic transport has been investigated in a two-dimensional mathematical model of peristalsis for the case when the wall of the channel executes a sinusoidal motion of small amplitude. Closed-form solutions have been obtained for limiting values of Reynolds number and the Poiseuille flow parameter, while the method of Frobenius series solution has been used for the general case. It is found that the mean flow reversal is strongly dependent on the Poiseuille flow. The position of flow reversal may change drastically from the center of the channel to the boundaries. Numberical results are reported for various values of the physical parameters of interest.
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    Enzyme kinetics in cells (1974)
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    Bulletin of mathematical biology 36 (1974), S. 157-169 
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    Notes: Abstract Classical enzymology ignores the role which cellular membranes may play in regulating reaction kineticsin vivo. The correct description of cellular metabolic processes must derive from a mass balance equation for each reacting species. An elementary mathematical model, called the “continuous flow stirred tank reactor” in the chemical engineering literature, has been applied to Michaelis-Menten kinetics, substrate inhibition kinetics, and kinetics involving hydrogen ion as a byproduct. A number of remarkable phenomena, including multiple stationary states, threshold effects, temporal patterns, homeostatic regulation, amplification, and irreversible differentiation can result. Predictions of the model are in qualitative accord with experimental and theoretical studies of insolubilized enzymes, which are conventionally modeled by a more difficult mathematical formalism.
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    Stability and enzyme separation: Integral representation of the solutions (1974)
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    Bulletin of mathematical biology 36 (1974), S. 197-203 
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    Notes: Abstract Two enzymes, cross-coupled through their respective products, are membrane-bound and thereby separated from each other. The cross-coupling is of opposite character and diffusion limited, i.e. an activation-inhibition couple with a diffusion-induced time-lag. In this paper an integral representation for the solutions of the dynamic equations is developed using the Green's function technique, and an application to morphological changes in the mitochrondrion is discussed.
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    Stochastic kinetic models for small irreversible systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 219-227 
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    Notes: Abstract The probability distribution of the process level is derived for a general class of irreversible reaction systems. A method of approximating the mean and variance of the process level is developed and shown to be more accurate for small irreversible systems than other approximations used in the stochastic approach to kinetics.
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    Semiconductor theory of ion transport in thin lipid membranes: I. Potential and field distributions (1974)
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    Bulletin of mathematical biology 36 (1974), S. 229-246 
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    Notes: Abstract In the theory as presented in this paper and the following one, we shall attempt to apply the semiconductor principles and methods to the study of ion transport in thin lipid membranes. Detailed formulations are given on the potential energy barriers at the interfaces, voltage drops in the polar and non-polar regions, and potential and field distributions in the diffuse double layer and within a charged membrane. These results will be used mainly as the boundary conditions for the solution of ion flow as to be given in the following paper. The analysis clearly indicates that the ion transport is interface-limited and is profoundly influenced by the presence of surface charges. An explanation of Na+ extrusion in nerve membrane is given based on the field distribution analysis. The theory also suggests that the “membrane potential” depends mainly on surface charges but not necessarily on ion permeation through the membrane.
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    Flagellar elongation as a moving boundary problem (1974)
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    Bulletin of mathematical biology 36 (1974), S. 265-273 
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    Notes: Abstract Movement of a proposed controlling factor along the growing flagellum is considered as a special case of one-dimensional diffusion with a moving boundary. Flagellar elongation, which involves polymerization of the building units at the distal tip, is viewed as taking place in a series of steps. The concentration of the controlling factor at the tip is computed as a function of the distance of the tip from the base, and the time between polymerization reactions. It is proposed that the concentration of this factor at the tip is responsible for regulating the flagellar growth rate and final length.
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    Stochastic theory of compartments (1974)
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    Bulletin of mathematical biology 36 (1974), S. 305-309 
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    Notes: Abstract The stochastic model of a compartment developed by Thakur, Rescigno and Schafer is discussed without using generating functions. The behavior of the mean and variance of the number of particles present as a function of time is also discussed. We also allow both the input and output to be time dependent.
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    A new model for interacting populations—I: Two-species systems (1974)
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    Bulletin of mathematical biology 36 (1974), S. 347-353 
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    Notes: Abstract The exact solvable model presented here describes two interacting species whose populations oscillate periodically in time in the absence of self-interaction and attain saturation with fluctuations if self-interactions are included. While sharing broad features of the classical Volterra system, the model proposed here has the advantage of possessing exact solutions. The model thus provides a testing ground for general principles employed in the study of dynamics of populations.
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    Terse reviews (1974)
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    Mathematical programming 6 (1974), S. 234-240 
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    A note on a theorem of F. Browder (1974)
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    Mathematical programming 6 (1974), S. 229-233 
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    Notes: Abstract A particular case of a mathematical theorem of F. Browder on the behavior of the fixed point set of a mapping under variations of a parameter has recently found applications in programming theory in connection with the abstract (non-linear) complementarity problem (see Eaves, [2, 3]). Two relevant extensions of Browder's result are provided: The first asserts that, under smoothness assumptions, the connected set of fixed points one gets from Browder's theorem is “generically” an arc; the second gives a generalization to the case where the mapping is an upper hemicontinuous contractible valued correspondence.
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    Editorial policy (1974)
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    Mathematical programming 6 (1974), S. 371-371 
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    On the convergence of SUMT (1974)
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    Mathematical programming 6 (1974), S. 360-364 
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    Notes: Abstract This paper investigates some convergence properties of Fiacco and McCormick's SUMT algorithm. A convex programming problem is given for which the SUMT algorithm generates a unique unconstrained minimizing trajectory having an infinite number of accumulation points, each a global minimizer to the original convex programming problem.
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    Packing rooted directed cuts in a weighted directed graph (1974)
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    Mathematical programming 6 (1974), S. 1-13 
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    Notes: Abstract A simple algorithm is described for constructing a maximum packing of cuts directed away from a distinguished vertex, called the root, in a directed graph, each of whose edges has a nonnegative weight, and it is shown that the maximum packing value is equal to the weight of a minimum-weight spanning arborescence directed away from the root.
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    On pricing and backward transformation in linear programming (1974)
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    Mathematical programming 6 (1974), S. 42-47 
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    Notes: Abstract In this paper we re-examine some of the available methods for pricing out the columns in the simplex method and point out their potential advantages and disadvantages. In particular, we show that a simple formula for updating the pricing vector can be used with some advantage in the standard product form simplex algorithm and with very considerable advantage in two recent developments: P.M.J. Harris' dynamic scaling method and the Forrest—Tomlin method for maintaining triangular factors of the basis.
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    On the existence of optimal solutions to integer and mixed-integer programming problems (1974)
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    Mathematical programming 7 (1974), S. 223-235 
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    Notes: Abstract The purpose of this paper is to present sufficient conditions for the existence of optimal solutions to integer and mixed-integer programming problems in the absence of upper bounds on the integer variables. It is shown that (in addition to feasibility and boundedness of the objective function) (1) in the pure integer case a sufficient condition is that all of the constraints (other than non-negativity and integrality of the variables) beequalities, and (2) that in the mixed-integer caserationality of the constraint coefficients is sufficient. Some computational implications of these results are also given.
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    Fenchel and Lagrange duality are equivalent (1974)
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    Mathematical programming 7 (1974), S. 253-258 
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    The Mathematical Programming Society (1974)
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    Mathematical programming 7 (1974), S. 262-262 
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    A bilinear programming formulation of the 3-dimensional assignment problem (1974)
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    Mathematical programming 7 (1974), S. 376-379 
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    On the selection of parameters in Self Scaling Variable Metric Algorithms (1974)
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    Mathematical programming 7 (1974), S. 351-367 
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    Notes: Abstract This paper addresses the problem of selecting the parameter in a family of algorithms for unconstrained minimization known as Self Scaling Variable Metric (SSVM) Algorithms. This family, that has some very attractive properties, is based on a two parameter formula for updating the inverse Hessian approximation, in which the parameters can take any values between zero and one. Earlier results obtained for SSVM algorithms apply to the entire family and give no indication of how the choice of parameter may affect the algorithm's performance. In this paper, we examine empirically the effect of varying the parameters and relaxing the line-search. Theoretical consideration also leads to a switching tule for these parameters. Numerical results obtained for the SSVM algorithm indicate that with proper parameter selection it is superior to the DFP algorithm, particularly for high-dimensional problems.
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    Book reviews (1974)
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    Mathematical programming 7 (1974), S. 388-388 
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    Note on an extension of “Davidon” methods to nondifferentiable functions (1974)
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    Mathematical programming 7 (1974), S. 384-387 
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    Notes: Abstract Some properties of “Davidon”, or variable metric, methods are studied from the viewpoint of convex analysis; they depend on the convexity of the function to be minimized rather than on its being approximately quadratic. An algorithm is presented which generalizes the variable metric method, and its convergence is shown for a large class of convex functions.
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    Trivial integer programs unsolvable by branch-and-bound (1974)
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    Mathematical programming 6 (1974), S. 105-109 
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    Editorial policy (1974)
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    Mathematical programming 6 (1974), S. 118-118 
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    Nested decomposition for dynamic models (1974)
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    Mathematical programming 6 (1974), S. 121-140 
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    Notes: Abstract This nested decomposition algorithm is intended for solving linear programs with the staircase structure that is characteristic of dynamic multi-sector models for economic development. Staircase problems represent a special case of the discrete-time optimal control problem. Our method is based upon the same principles as that of Glassey [5], but appears easier to describe and to relate to control theory. Computational experience is reported for a series of test problems. The algorithm has been coded in MPL, an experimental language for mathematical programming. This translator has made it possible to obtain a more readable program — and with fewer instructions — than one written in a conventional language. However, because the present version of MPL does not permit the use of slow access memory, this has prevented us from exploring the full potential of nested decomposition for solving larger problems than can be handled by conventional simplex techniques.
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    Modified regularity conditions for nonlinear programming problems over mixed cone domains (1974)
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    Mathematical programming 6 (1974), S. 167-179 
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    Notes: Abstract In earlier results by Sposito and David, Kuhn—Tucker duality was established over nondegenerate cone domains (not necessarily polyhedral) without differentiability under a certain natural modification of the Slater condition, in addition to the convexity of a certain auxiliary set. This note extends Kuhn—Tucker duality to optimization problems with both nondegenerate and degenerate cone domains. Moreover, under a different condition than presented in earlier results by the author, this note develops Kuhn—Tucker duality for a certain class of nonlinear problems with linear constraints and an arbitrary objective function.
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    Editorial policy (1974)
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    Mathematical programming 7 (1974), S. 260-261 
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    Coefficient reduction for inequalities in 0–1 variables (1974)
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    Mathematical programming 7 (1974), S. 263-282 
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    Notes: Abstract For a given inequality with 0–1 variables, there are many other “equivalent” inequalities with exactly the same 0–1 feasible solutions. The set of all equivalent inequalities is characterized, and methods to construct the equivalent inequality with smallest coefficients are described.
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    A complementary variant of Lemke's method for the linear complementary problem (1974)
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    Mathematical programming 7 (1974), S. 283-310 
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    Notes: Abstract An algorithm for the linear complementarity problem is developed which uses principal pivots only. The algorithm is shown to be equivalent to Lemke's algorithm. The advantage of the proposed algorithm is that infeasibility tests may be made after each principal pivot. One such test is equivalent to a check whether the matrix satisfies the “plus” condition of copositive plus matrices or the condition of classL 2 of Eaves.
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    A “from scratch” proof of a theorem of Rockafellar and Fulkerson (1974)
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    Mathematical programming 7 (1974), S. 368-375 
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    Notes: Abstract The theorem of this paper is of the same general class as Farkas' Lemma, Stiemke's Theorem, and the Kuhn—Fourier Theorem in the theory of linear inequalities. LetV be a vector subspace ofR n , and let intervalsI 1,⋯, I n of real numbers be prescribed. A necessary and sufficient condition is given for existence of a vector (x 1 ,⋯, x n ) inV such thatx i ∈I i (i = 1, ⋯,n); this condition involves the “elementary vectors” (nonzero vectors with minimal support) ofV ⊥. The proof of the theorem uses only elementary linear algebra.
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    Back volumes Mathematical Programming (1974)
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    Mathematical programming 7 (1974), S. 389-389 
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    Editorial policy (1974)
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    Mathematical programming 7 (1974), S. 390-390 
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    Minimality and complementarity properties associated with Z-functions and M-functions (1974)
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    Mathematical programming 7 (1974), S. 17-31 
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    Notes: Abstract A nonlinear generalization of square matrices with non-positive off-diagonal elements is presented, and an algorithm to solve the corresponding complementarity problem is suggested. It is shown that the existence of a feasible solution implies the existence of a least solution which is also a complementary solution. A potential application of this nonlinear setup in extending the well-known linear Leontief input—output systems is discussed.
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    A monotonic passy-like algorithm for the modular design problem (1974)
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    Mathematical programming 7 (1974), S. 46-59 
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    Notes: Abstract This paper presents a new algorithm for the continuous modular design problem. The method is based on and can be combined with preceding work by Passy, and Shaftel and Thompson. The proposed algorithm guarantees a strict decrease of the objective function's value at every iteration and converges in a finite number of steps.
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    Closed ideals in subalgebras of Banach algebras II: Ditkin's condition (1974)
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    Monatshefte für Mathematik 78 (1974), S. 1-3 
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    Lösung der formalen Potenzreihene A e B =e X unde A+Bt =e A e X (1974)
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    Monatshefte für Mathematik 78 (1974), S. 4-14 
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    Funktoren auf Kategorien von Banachräumen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 15-24 
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    Poissonmaße auf lokalkompakten Halbgruppen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 25-41 
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    Lürothsche Reihen und singuläre Maße (1974)
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    Monatshefte für Mathematik 78 (1974), S. 42-50 
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    Ein Problem aus der Theorie der Gleichverteilung. I. Teil (1974)
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    Monatshefte für Mathematik 78 (1974), S. 51-67 
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    Über endliche, ordnungspolynomvollständige Verbände (1974)
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    Monatshefte für Mathematik 78 (1974), S. 68-76 
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    Ein Eindeutigkeitssatz bei Funktional-Differentialgleichungen mit unendlicher Nacheilung (1974)
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    Monatshefte für Mathematik 78 (1974), S. 77-82 
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    Buchbesprechungen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 83-96 
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    Begleitsphären windschiefer Flächen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 97-108 
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    Der Defekt endlicher abelscher Gruppen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 109-116 
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    Zum Tensorprodukt von Funktoren auf Kategorien von Banachräumen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 117-130 
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    Eine diophantische Approximations-Funktion (1974)
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    Monatshefte für Mathematik 78 (1974), S. 131-146 
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    Erzeugung äquivalenter Summierungsverfahren durch Matrizenprodukte (1974)
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    Monatshefte für Mathematik 78 (1974), S. 147-155 
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    Über die endlichen Ringe mit gegebener additiver Gruppe (1974)
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    Monatshefte für Mathematik 78 (1974), S. 164-173 
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    Asymptotische Abschätzung einer Anzahlfunktion in endlichen Relationssystemen (1974)
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    Monatshefte für Mathematik 78 (1974), S. 174-180 
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