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  • 1
    Electronic Resource
    Electronic Resource
    Multibreath tracer species dynamics in the lung (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460935
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  • 2
    Electronic Resource
    Electronic Resource
    Global stability of population models (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460938
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  • 3
    Electronic Resource
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    The logistic equation with a diffusionally coupled delay (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459438
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  • 4
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    Uncertainty in physiology and physics (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 141-149 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459439
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  • 5
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    Consensusn-trees (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 239-244 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459446
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  • 6
    Electronic Resource
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    Morphogen pattern formation and development in growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 259-270 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462200
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  • 7
    Electronic Resource
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    Simulation experiments with a model for cellular growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 271-278 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462201
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  • 8
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    Complementary extremum principles for a nonlinear model of heat conduction in the human head (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 341-346 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462204
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  • 9
    Electronic Resource
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    On Zeeman's equations for the nerve impulse (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 279-325 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
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    URL: http://dx.doi.org/10.1007/BF02462202
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  • 10
    Electronic Resource
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    Asymptotic analysis of the Michaelis-Menten reaction equations (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 375-388 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459428
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  • 11
    Electronic Resource
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    Pulse evolution on coupled nerve fibres (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 389-400 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
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    URL: http://dx.doi.org/10.1007/BF02459429
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  • 12
    Electronic Resource
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    Field-induced forces at dielectric interfaces as a possible mechanism of RF hearing effects (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 401-413 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
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    URL: http://dx.doi.org/10.1007/BF02459430
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  • 13
    Electronic Resource
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    The construction of homogeneous nets (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 415-426 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459431
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  • 14
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    Contractile analysis and kinetic energy of the myocardium (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
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    URL: http://dx.doi.org/10.1007/BF02459433
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  • 15
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    Limit cycles in periodically perturbed population systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 463-485 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
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    URL: http://dx.doi.org/10.1007/BF02459434
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  • 16
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    On a unified approach to pattern generation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 513-516 
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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/BF02459437
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  • 17
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    Limits on the computing power of biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 59-67 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.
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    URL: http://dx.doi.org/10.1007/BF02460939
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  • 18
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    A topological study of the base sequences of MS2 and ϕX174 genoma (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 81-88 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460941
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  • 19
    Electronic Resource
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    Volume of the conducting airways calculated from morphometric parameters (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 101-109 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460943
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  • 20
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    Variability in a single compartment system: A note on S. R. Bernard's model (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 111-116 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460944
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  • 21
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    The diffusion transit time; A simple derivation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 89-99 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.
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    URL: http://dx.doi.org/10.1007/BF02460942
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  • 22
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    Nonlinear oscillations in biology (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 121-123 
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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/BF02460946
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  • 23
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    A comment on Lin's paper on nonlinear diffusion in biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 117-120 
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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/BF02460945
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  • 24
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    On the stochastic theory of compartments: The leaving process of the two-compartment systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 201-211 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.
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    URL: http://dx.doi.org/10.1007/BF02459443
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  • 25
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    Models on prebiotic polymer competition: A deterministic approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 213-232 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.
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    URL: http://dx.doi.org/10.1007/BF02459444
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  • 26
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    Extinction probabilities in microbial predation: A birth and death approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 165-181 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.
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    URL: http://dx.doi.org/10.1007/BF02459441
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  • 27
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    Prediction of the effect of the choroidal circulation on the retinal temperature during illumination (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 233-238 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.
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    URL: http://dx.doi.org/10.1007/BF02459445
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  • 28
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    Spatially localized interactive neural populations—I. A mathematical model (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 427-446 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.
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    URL: http://dx.doi.org/10.1007/BF02459432
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  • 29
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    A one-compartment model with stochastic parameter (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 503-512 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.
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    URL: http://dx.doi.org/10.1007/BF02459436
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  • 30
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    A dose-response model for estimating lifetime tumor risks when cell killing occurs (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 487-501 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.
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  • 31
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    A stochastic model for then-compartment irreversible system (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 549-561 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.
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    URL: http://dx.doi.org/10.1007/BF02462312
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  • 32
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    Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 563-577 
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    Notes: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.
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    Dynamic structure theory: A structural approach to social and biological systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 579-591 
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    Notes: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
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    Peak drug levels in linear pharmacokinetic systems—II. Conditions for a paradoxical injection rate effect with rectangular input (1981)
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    Bulletin of mathematical biology 43 (1981), S. 705-715 
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    Notes: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.
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    Peak drug levels in linear pharmacokinetic systems—I. Effect of rate of injection (1981)
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    Bulletin of mathematical biology 43 (1981), S. 693-703 
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    Notes: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.
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    On a two urn model of Polya-type (1981)
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    Bulletin of mathematical biology 43 (1981), S. 33-45 
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    Notes: Abstract A two urn Polya-type scheme is considered in whichr black balls (corresponding to the stable form of an element) are added to urn one at every stage and the same number of balls are removed at random at every stage from the same urn. In between these two operations, which form a stage or iteration, a fixed number of balls is exchanged at random between urns one and two. Urn one has a given initial number of white balls (corresponding to a radioactive form of the same element). The problem of interest is to study the stochastic aspect of the number of white balls remaining in urn one (and/or urn two) aftern iterations.
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    Nonlinear biological oscillators: Action-angle variable approach with an application to Cowan's model of neuroelectric activity (1981)
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    Bulletin of mathematical biology 43 (1981), S. 21-32 
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    Notes: Abstract We obtain within the action-angle variable approach new expressions, involving the Dirac delta function, for time periods and time averages of dynamical variables which are useful for nonlinear biological oscillator problems. We combine these with Laplace transformation techniques for evaluating the required perturbation expansions. The radii of convergence of these series are determined through a complex variable approach. The method is powerful enough to yield explicit results for such systems as the two species Volterra model, Goodwin's model of protein synthesis etc. and as an illustration, is applied here to Cowan's model of neuroelectric activity. We also point out the usefulness of the action integral in the case where parameters occurring in dynamics have slow time variations.
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    A generalized Fokker-Planck equation in the case of the Volterra model (1981)
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    Bulletin of mathematical biology 43 (1981), S. 69-79 
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    Notes: Abstract Zwanzig and Mori's projection-operator method is used in order to derive a generalized nonlinear Fokker-Planck equation for one “relevant” species in the many species conservative Volterra model. The deterministic, autonomous, Markovian equations of motion, when averaged over a suitable ensemble of initial conditions in general give rise to a non-autonomous, non-Markovian stochastic process for the evolution of this relevant species. Moreover, this relevant species may show irreversible damping, although self-interaction terms are absent in the many species model.
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    A hydrodynamical study of the flow in renal tubules (1981)
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    Bulletin of mathematical biology 43 (1981), S. 151-163 
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    Notes: Abstract The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.
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    Some comments on the conductance of slow inward current in cardiac muscle (1981)
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    Bulletin of mathematical biology 43 (1981), S. 183-199 
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    Notes: Abstract Voltage clamp experiments, which determine the kinetic parameters of calcium conductance of cardiac muscle, (d ∞,f ∞, τ d and τ f ) are analyzed with a generally accepted expression for slow inward currentI s=g sdf (E-E R). Activation (d) and inactivation (f) reach the final valuesd ∞ andf ∞ with time constants τ d and τ f respectively. The analysis indicates that the measuredf ∞ agrees with the theoreticalf ∞, but the measuredd ∞ differs from the theoreticald ∞ by a factor which depends on τ d . The peak tension can be made to correlate closely with the theoreticald ∞ after a correction factor is applied to the raw measurements of activation. It can be shown that experiments designed to measure τ f can also be used to determine τ d with greater accuracy.
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    On the relevance of stochastic compartmental models to pharmacokinetic systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 245-247 
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    Identification of silent infections in SIR epidemics (1981)
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    Bulletin of mathematical biology 43 (1981), S. 249-257 
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    Notes: Abstract A deterministic model for an SIR epidemic with silent infections is investigated. It is shown for the model studied that the extent to which silent infections are present may be determined from data concerning only those individuals with symptomatic infection.
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    A reinforcement-depletion urn problem—I. Basic theory (1981)
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    Bulletin of mathematical biology 43 (1981), S. 327-340 
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    Notes: Abstract An urn contains balls of different colors. Specified numbers of each color are added and form a reinforcement. The total reinforcement is randomly removed, forming a depletion. The process, not necessarily with the same reinforcements, is performed a number of times. The factorial moment generating function of the urn configurations at any stage is given in terms of multivariate difference operators. Cases when the reinforcement vector is defined as a stochastic variable are considered. The problem is a generalization of an urn model associated with radioactive atoms and stable atoms proposed by S. R. Bernard. The solutions given here have a definite application to the problem of modelling tracers in compartmental systems.
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    Stochastic compartmental model with branching particles (1981)
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    Bulletin of mathematical biology 43 (1981), S. 347-360 
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    Notes: Abstract A multi-compartmental model with particles producing offspring according to the Markov branching process has been studied. Explicit results are given for the two-compartmental system and for irreversible general multicompartmental systems. The known models in stochastic compartmental analysis are shown to be particular cases of this model and applications are cited.
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    On Wei's fundamental equation for nerve excitation (1981)
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    Bulletin of mathematical biology 43 (1981), S. 371-372 
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    Phase-plane analyses of the Michaelis-Menten reaction equations (1981)
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    Bulletin of mathematical biology 43 (1981), S. 361-370 
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    Notes: Abstract The irreversible Michaelis-Menten scheme may be reduced to a pair of autonomous first-order differential equations. The phase-plane behaviour of these is investigated.
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    Reply to Chyuan-Yih Lee (1981)
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    Bulletin of mathematical biology 43 (1981), S. 372-373 
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    Further considerations in a theoretical description of gas transport in lung airways (1981)
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    Bulletin of mathematical biology 43 (1981), S. 517-548 
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    Notes: Abstract A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe〈1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O2 concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.
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    Effects of convective and dispersive interactions on the stability of two species (1981)
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    Bulletin of mathematical biology 43 (1981), S. 593-610 
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    Notes: Abstract The evolution and local stability of a system of two interacting species in a finite two-dimensional habitat is investigated by taking into account the effects of self- and cross-dispersion and convection of the species. In absence of cross-dispersion, an equilibrium state which is stable without dispersion is always stable with dispersion provided that the dispersion coefficients of the two species are equal. However, when the dispersion coefficients of the two species are different, the possibility of self-dispersive instability arises. It is also pointed out that the cross-dispersion of species may lead to stability or instability depending upon the nature and the magnitude of the cross-dispersive interactions in comparison to the self-dispersive interactions. The self-convective movement of species increases the stability of the equilibrium state and can stabilize an otherwise unstable equilibrium state. The effect of cross-convection (in absence of self-dispersion and self-convection) is to stabilize the equilibrium state in a prey-predator model with positive cross-dispersion coefficients for the prey species. Finally, it is shown that if the system is stable under homogeneous boundary conditions it remains so under non-homogeneous boundary conditions.
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    Role of the hypergeometric distribution in the transmission of excitation through sympathetic ganglia (1981)
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    Bulletin of mathematical biology 43 (1981), S. 611-618 
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    Notes: Abstract Various observations suggest that sympathetic ganglia act as local integrative centers redistributing preganglionic excitation (i.e. the information issued by the central nervous system) to the postganglionic fibers (and effector organs). In order to support this concept a simple mathematical model of the elementary integration process, treating the case of a single preganglionic compound action potential, has been developed. This quantitative description, based on a few elementary assumptions, shows a possible way of processing preganglionic excitation in the ganglion. It is shown that on a particular ganglion cell the probability distribution of the number of activated synapses obeys hypergeometric distribution and hence, the postganglionic compound action potential is built up of several compound action potentials occurring at different times. The former correspond to different groups of firing cells. The model discloses modes of structural and temporal pattern generation performed by the sympathetic ganglion.
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    The uniqueness of protein sequences: A Monte Carlo analysis (1981)
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    Bulletin of mathematical biology 43 (1981), S. 619-639 
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    Notes: Abstract Amino acid sequences have already been examined in some detail in order to relate them to structural aspects, homology and gene duplication. This report introduces the concept of internal uniqueness of tripeptides within protein sequences and uses the Monte Carlo method to study this property. Some idea of internal uniqueness may be obtained from such an analysis using only a single sequence if the probability of the random occurrence is about 0.001 or less. This method of analysis is similar to that used in quantitative evaluations of homology. When the probability of the random occurrence is larger than 0.001 a homologous group of sequences is required and the random probabilities may be compared with the real occurrences within the group. From such an examination insulin and cytochrome c are identified as protein sequences with high internal uniqueness. A comparison of data from internal uniqueness and gene duplication analyses shows that these two properties need not be related. Results of the analysis point to internal uniqueness as an additional parameter for inclusion in speculations on why twenty amino acids are coded in protein structure.
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    Tolerance nets (1981)
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    Bulletin of mathematical biology 43 (1981), S. 641-650 
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    Notes: Abstract The concept of a tolerance net formalises simultaneously spatial closeness and nearness of neuronal activity. A method of constructing tolerance group nets is presented, leading to a means of construction of all very homogenous tolerance nets as group quotients. The dihedral group of order eight is taken as an illustrative example.
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    Relation between diameter and flow in branches of the bronchial tree (1981)
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    Bulletin of mathematical biology 43 (1981), S. 681-691 
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    Notes: Abstract Two methods are described for calculating the value of the exponentx in the equation flow =k×diameter x , as pertaining to a branch of the bronchial tree. In the lungs from three humans, two dogs, one hamster, and one rat mean values ofx between 2.419 and 2.903 were found. They lie within the range of 2.333 to 3.0 predicted by the analysis of Uylings (Bull. Math. Biol. 39, 501–519, 1977).
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    Stochastic analysis of a nonlinear model for selection of biological macromolecules (1981)
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    Bulletin of mathematical biology 43 (1981), S. 665-680 
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    Notes: Abstract A stochastic analysis of a nonlinear selection model is presented. The model, based on Eigen and Schuster's theory of selection and evolution of biological macromolecules, considers the effects of fluctuations on the individual concentrations of macromolecules as well as the total population numbers in constrained systems. Our analysis shows that one of the models most often treated deterministically (referred to as constant organization in the literature) becomes unstable when fluctuations in the total population number are considered. An alternative model which apparently has built in self-regulating properties is analyzed and proves to be stable except for some special cases of degeneracy.
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    Compartmental models with multiple sources of stochastic variability: The one-compartment models with clustering (1981)
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    Bulletin of mathematical biology 43 (1981), S. 651-664 
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    Notes: Abstract Previous compartmental models have introduced variability either at the particle or at the replicate level. This paper integrates both types of variability through the concept of clustering. The paper develops two different, general clustered models, each with time-dependent hazard rates for the clusters and for the particles within the clusters, and each with random initial number and sizes of clusters. The coefficient of variation of the total number of particles,CV[X(t)], for either model is shown to be bounded below, under very broad conditions, by the coefficient of variation of the initial number of clusters,CV[c(0)]. This high relative variability of the clustered models makes them potentially very useful in kinetic modeling. In many applications, binding and clustering are common phenomena, and two applications of the models to such phenomena are breifly outlined.
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    Some trees are not interval graphs (1981)
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    Bulletin of mathematical biology 43 (1981), S. 717-717 
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    Annual Meeting of the Cell Kinetics Society (1981)
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    Bulletin of mathematical biology 43 (1981), S. 719-719 
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    On the number of solutions to a class of complementarity problems (1981)
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    Mathematical programming 21 (1981), S. 190-203 
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    Keywords: Complementarity Problem ; Cones ; Topological Degree
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    Notes: Abstract In this paper we consider the problem of establishing the number of solutions to the complementarity problem. For the case when the Jacobian of the mapping has all principal minors negative, and satisfies a condition at infinity, we prove that the problem has either 0, 1, 2 or 3 solutions. We also show that when the Jacobian has all principal minors positive, and satisfies a condition at infinity, the problem has a unique solution.
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    Finding simplicial subdivisions of polytopes (1981)
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    Mathematical programming 21 (1981), S. 233-234 
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    Keywords: Polytope ; Subdivision ; Simplex ; Volume ; Centroid
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    Notes: Abstract Subdivisions of polytopes are described which place any chosen vertex in a (near-) minimal number of simplices. Ancillary procedures to find volumes and centroids of polytopes are indicated.
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    Direct theorems in semi-infinite convex programming (1981)
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    Mathematical programming 21 (1981), S. 301-318 
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    Keywords: Semi-infinite Programs ; Open Helly-type Theorems ; Finite Subprograms ; Convex Programs ; Multi-criteria Programs ; Quasi-convex Programs ; Quasi-differentiable Programs
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    Notes: Abstract We show that a semi-infinite quasi-convex program with certain regularity conditions possesses finitely constrained subprograms with the same optimal value. This result is applied to various problems.
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    A statistical estimate of the structure of multi-extremal problems (1981)
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    Mathematical programming 21 (1981), S. 348-356 
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    Keywords: Multi-extremal Optimization ; Multinomial Distribution ; Bayes Estimate ; Monte Carlo
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    Notes: Abstract The solution of ak-extremal problem is defined as the set of pairs (x i * , θi),i = 1, ⋯ ,k, where x t * isi th local minimum andθ i is the volume of the set of attraction of this minimum. A Bayesian estimate ofk and (θ 1 , ⋯ , θ k ) is constructed.
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    Symposium on network flows (1981)
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    Mathematical programming 21 (1981), S. 120-120 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01584234
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    On solving a primal geometric program by partial dual optimization (1981)
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    Mathematical programming 21 (1981), S. 319-330 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Geometric Programming ; Duality Theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The several published methods for mapping a dual solution estimate to a primal solution estimate in posynomial geometric programming provide no criteria for deciding how much deviation from primal feasibility, or discrepancy between the primal and dual objective function values, should be permitted before the primal solution estimate is accepted by the designer. This paper presents a new and simple dual-to-primal conversion method that uses the cost coefficients to provide a sound economic criterion for determining when to accept a primal solution estimate. The primal solution estimate generated is the exact solution to a modified primal obtained from the given primal by modifying the cost coefficients, with the exponent matrix left unchanged. The method is shown to have desirable properties when coupled with a convergent dual algorithm.
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    Minimum cost spanning tree games (1981)
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    Mathematical programming 21 (1981), S. 1-18 
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    ISSN: 1436-4646
    Keywords: Game Theory ; Cost Allocation ; Spanning Tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.
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    Institute on deterministic and stochastic scheduling (1981)
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    Mathematical programming 21 (1981), S. 119-119 
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    Source: Springer Online Journal Archives 1860-2000
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    URL: http://dx.doi.org/10.1007/BF01584233
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    Polynomial algorithms for a class of linear programs (1981)
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    Mathematical programming 21 (1981), S. 121-136 
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    ISSN: 1436-4646
    Keywords: Linear Programming ; Polynomial Algorithms ; Total Unimodularity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes several algorithms for solution of linear programs. The algorithms are polynomial when the problem data satisfy certain conditions.
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    An algorithm for computing equilibria in a linear monetary economy (1981)
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    Mathematical programming 21 (1981), S. 182-189 
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    ISSN: 1436-4646
    Keywords: Equilibrium ; Linear Monetary Economy ; Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An algorithm is presented for computing equilibria in a linear monetary economy, that is, an exchange economy in which all individuals have linear utility functions and in which goods are bought and sold only in exchange for money. The algorithm computes the equilibrium prices by solving a finite sequence of linear programming problems.
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    Comment on a paper by M.C. Cheng (1981)
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    Mathematical programming 21 (1981), S. 229-232 
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    Keywords: Primal Feasible Basis ; Dual Feasible Basis ; Basic Variable ; Nonbasic Variable ; Optimal Basic Solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In a recent paper M.C. Cheng proposed new criteria for the simplex algorithm which guarantee that (i) a nonbasic variable of a basic feasible solution will remain nonbasic in an optimal basic solution, (ii) a basic variable of a basic solution will remain basic in an optimal basic solution. This comment gives (i) a slight generalization of the first result and (ii) a counterexample to the second proposition.
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    Euro V — tims XXV (1981)
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    Mathematical programming 21 (1981), S. 240-240 
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    URL: http://dx.doi.org/10.1007/BF01584247
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    An elementary survey of general duality theory in mathematical programming (1981)
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    Mathematical programming 21 (1981), S. 241-261 
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    ISSN: 1436-4646
    Keywords: Dual problem ; Duality Theory ; Optimality Conditions ; Price Functions ; Nonlinear Programming ; Integer Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We survey some recent developments in duality theory with the idea of explaining and unifying certain basic duality results in both nonlinear and integer programming. The idea of replacing dual variables (prices) by price functions, suggested by Everett and developed by Gould, is coupled with an appropriate dual problem with the consequence that many of the results resemble those used in linear programming. The dual problem adopted has a (traditional) economic interpretation and dual feasibility then provides a simple alternative to concepts such as conjugate functions or subdifferentials used in the study of optimality. In addition we attempt to make precise the relationship between primal, dual and saddlepoint results in both the traditional Lagrangean and the more general duality theories and to see the implications of passing from prices to price functions. Finally, and perhaps surprisingly, it appears that all the standard algorithms terminate by constructing primal and dual feasible solutions of equal value, i.e., by satisfying generalised optimality conditions.
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    International symposium on the occasion of the 25th anniversary of the econometric institute, rotterdam (1981)
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    Mathematical programming 21 (1981), S. 358-358 
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    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01584256
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    The connection between the measured glass transition temperature and the time dependent order parameter description of the glass transition (1981)
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    Polymer bulletin 5 (1981), S. 597-601 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The time dependent order parameter concept of the glass transition is used in a description of the relaxation behaviour of the glassforming material. The connection between the macroscopic theory and the measured glass transition temperature has been determined. It has been found that in a case when the Prigogine-Defay ratio is greater than unity, different values of the relaxation functions of entropy and volume obtained by different experiments (e.g., isobaric dilatometry and isothermal compression) should be used in order to obtain the identical Tg. The Prigogine-Defay ratio is found to be a decreasing function of the observation time reaching values between unity in the limit of infinite time and a limit which corresponds to extremely short experiments.
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    Separation of styrene oligomers by Supercritical Fluid Chromatography (SFC) using a modified HPCL-instrument (1981)
    Springer
    Polymer bulletin 5 (1981), S. 603-608 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary An instrument for High Performance Liquid Chromatography (HPLC) was modified by relatively simple means for working in the field of Supercritical Fluid Chromatography (SFC). By use of this modified apparatus three different gradient methods were tried with respect to their applicability for the analytical separation of oligomers. Especially by using a gradient in eluent composition or by a pressure gradient good resolution could be obtained.
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    Synthesis of ABA triblock copolymers containing electrono-donor or electrono-acceptor pendant groups in A blocks (1981)
    Springer
    Polymer bulletin 5 (1981), S. 643-649 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary α,ω-p-Toluensulphonic acid ester of poly(ethyleneglycoladipate) was synthesized and used to initiate the cationic isomerization polymerization of 2-phenyl-2-oxazoline, 2-(β-N-Carbazolylethyl)-2-oxazoline and 2-(3,5-dinitrophenyl)-2-oxazoline. ABA triblock copolymers containing poly(N-benzoylethylenimine), poly [N-β(N-carbazolyl)propionyl ethyleneimine] or poly(3,5-dinitrobenzoylethylenimine) blocks (A block) and poly (ethyleneglycoladipate) blocks (B block) have been synthesized.
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    Effect of nucleating agents upon the kinetics of polybutene-1 crystallization (1981)
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    Polymer bulletin 5 (1981), S. 635-641 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The influence of various nucleating agents on the crystallization parameters of polybutene-1 is reported. Isothermal crystallization is investigated by differential scanning calorimetry. The morphology induced by the differents nucleating agents has been observed by hot stage polarizing microscopy. It has been stated that the addition of nucleating agent affects the crystallization rate, dimension and homogeneity of spherulitic sizes. The induction time ti, the semicrystallization time t1/2, the crystallization rate constant K, and the Avrami coefficient n were measured and related to the different characteristics of the specimens. Because of the fractional values of n obtained in this study, it is not possible to propose well determined mechanisms of crystallization.
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    NMR study on phase transitions in lyotropic liquid crystals caused by hydrophobic additives (1981)
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    Polymer bulletin 5 (1981), S. 667-672 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Broad line NMR spectra have been measured at room temperature of the binary system Arkopal (C9H19C6H4O(CH2CH2O)15H) -heavy water (40 % to 60 % by weight) and of the ternary systems Arkopal — heavy water — paraffin at different paraffin concentrations at constant Arkopal — heavy water ratio. It has been established how the additives change the lyotropic phases.
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    Plasma-induced polymerization (1981)
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    Polymer bulletin 5 (1981), S. 61-66 
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    Notes: Summary Investigations carried out in plasma-induced polymerization (copolymerization) led to the idea of the existence of “living” macroradicals. Their presence in both homogeneous and heterogeneous media was experimentally proved and theoretically explained and their use as macromolecular initiators in polymerization processes is exemplified.
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    Physico-chemical studies of polymeric carriers: 2. Molecular mass determination of poly(N-vinylpyrrolidone-co-maleic acid) fractions (1981)
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    Polymer bulletin 5 (1981), S. 673-677 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Critical interpretation of the various conceptions concerning the problems in characterization of linear polyelectrolyte type polymers containing maleic acid as a comonomer is given. Proper conditions to avoid the fundamental experimental difficulties are proposed. Our conception is supported by molecular light scattering measurements of hydrolysed, fractionated poly (N-vinylpyrrolidone-co-maleic anhydride) samples. It was found that the problems were eliminated by the reduction of the degree of dissociation of carboxyl groups to a minimum value.
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    Relationship between preferential adsorption coefficient and intrinsic viscosity in ternary systems (1981)
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    Polymer bulletin 5 (1981), S. 67-74 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The relation proposed between the preferential adsorption coefficient, λ, and the intrinsic viscosity, ¦η¦ λ¦η¦=λ∞¦η¦+AKθ has been applied in this paper to previously published data. This equation is found to be valid in theta condi tions and far away from them. The obtained results are compared to the ones calculated with the Dondos-Benoit equation.
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    Acid and enzymic hydrolysis of Kappa carrageenan (1981)
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    Polymer bulletin 5 (1981), S. 81-86 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary This paper describes the acid and enzymic hydrolysis of Kappa carrageenan and the gel permeation chromatography of the charged oligosaccharides.
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    An empirical model for the melt viscosity of polymer blends (1981)
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    Polymer bulletin 5 (1981), S. 75-80 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary On the basis of experimental data for blends of polyethylene with different polymers an empirical equation is proposed to describe the dependence of melt viscosity of blends on component viscosities and composition. The model ensures the continuity of viscosity vs. composition curves throughout the whole composition range, the possibility of obtaining extremum values higher or lower than the viscosities of components, allows the calculation of flow curves of blends from the flow curves of components and their volume fractions.
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    Water vapor absorption and aqueous retention of hydrolyzed starch polyacrylonitrile graft copolymers — “superabsorbent starch” (1981)
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    Polymer bulletin 5 (1981), S. 87-94 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Starch copolymers with polyacrylonitrile grafts were prepared using the Mn3+ initiation method and different amounts of acrylonitrile. The product was hydrolyzed in aqueous alkali (nitrile groups to amide and carboxyl groups) to enhance the hydrophilic character of the copolymer and achieve “superabsorbent properties”. At relative humidities (RH) up to 95–97 % the modified starch shows “normal” water vapor absorption like cellulose and other polysaccharides. When in contact with liquid distilled water, the modified starch forms a “superabsorbent” gel which retains very large amounts of water (up to 800 g/g). At low and high pH and in aqueous salt solutions (NaCl, CaCl2 and synthetic urine) the water retention is strongly reduced. This is interpreted as due to the ionic strength (salt effect) and for Ca2+ ions probably also crosslinking by salt formation with carboxyl groups on adjacent chains or chain segments.
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    Rigid backbone polymers (1981)
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    Polymer bulletin 5 (1981), S. 95-101 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary It is shown that the inverse velocity of a fallingball in, or ηm the apparent minimum viscosity of, anisotropic solutions of poly(n-hexylisocyanate) in toluene, are molecular weight dependent. The molecular weight dependence follows two linear branches. Below Mw=42600 the apparent minimum viscosity is very weakly dependent on Mw. Above Mw=42600 the apparent minimum viscosity of the anisotropic solution is strongly dependent on the molecular weight.
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    Chemical modification of polystyrene (1981)
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    Polymer bulletin 5 (1981), S. 111-116 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Sulfinate functional groups have been introduced on selected positions of the aromatic rings of soluble or crosslinked polystyrene via lithiation reactions followed by quenching with sulfur dioxide. The sulfinate polymers have good stability, can be stored at room temperature, and can be used for ion-exchange or as nucleophiles to produce polymer-bound sulfones. Good functional yields of polystyrene resins with sulfone pendant groups can be obtained by reaction of the polymeric sulfinates with various alkyl halides under phase transfer or classical conditions.
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    A kinetic study of crosslinking vinyl polymerization by laser Raman spectroscopy (1981)
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    Polymer bulletin 5 (1981), S. 103-110 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Kinetic studies of crosslinking vinyl polymerizations are usually only applicable to the initial stages of the reaction, prior to the gel point, due to the subsequent insolubility of the polymer and the great increase in viscosity. We have demonstrated the suitability of laser Raman spectroscopy for quantitative analysis over the entire conversion range in an investigation of the polymerization of diethylene glycol bis (allyl carbonate) in bulk, with benzoyl peroxide initiation, between 70 and 85°C. The rate of consumption of vinyl bonds could be approximated by first-order kinetics up to ca. 80% depletion. Lower rates were observed at higher conversions.
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    Correction (1981)
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    Polymer bulletin 5 (1981), S. 117-117 
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    A modification of rubber elasticity theory (1981)
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    Polymer bulletin 5 (1981), S. 151-157 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Based on a reconsideration of the packing conditions in amorphous polymers, a modification of the statistical theory of rubber elasticity is derived. The main assumption is, that the mean square end-to-end distance of a free chain in the bulk state depends on the dimensions of the surrounding chains. The theory describes quite well the deformation behaviour of real elastomeric networks.
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    Micro- and macroconformation of macromolecules (1981)
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    Polymer bulletin 5 (1981), S. 131-135 
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    Notes: Summary Cyclotetracosane exhibits complex phase behaviour in the solid state as well as in the melt as evidenced by complementary methods, DSC, BRILLOUIN scattering, dielectric constant and PE-MAS 13c-NMR. Three solid phases have been verified, one of them — within the range from 299.5 to 312 K — exhibits extremely high molecular mobility. Between the start of melting, 312 K, and the first order transition at ∼ 321 K a mesomorphic type region develops. Two additional transitions have been detected in the melt. That occuring at 361 K (DSC), 356 K (BRILLOUIN data) resembles the Tu as observed in n-alkanes.
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    Synthesis, characterization and polycondensation of Bis-(4-hydroxybutyl) terephthalate (1981)
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    Polymer bulletin 5 (1981), S. 159-166 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Monomeric Bis-(4-hydroxybutyl) terephthalate has been synthesized and characterized. Titanium iso-propoxide has been found to be a superior catalyst for transesterification compared to metal acetates. Further polycondensation of Bis (HBT) yields poly (1,4-butylene terephthalate). The effect of various titanium derived catalysts on the polycondensation of Bis (HBT) has been studied. The catalytic efficiency of these derivatives is ascribed to their relative hydrolytic stability and the degree of interaction between the carbonyl oxygen and the metal.
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    On the PVC chlorination mechanism (1981)
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    Polymer bulletin 5 (1981), S. 167-174 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A radiochemical method was used to study PVC chlorination. A reaction mechanism was proposed based on the results obtained from chlorination of 36chlorine labeled PVC. A mechanism was proposed also for chain transfer reaction to polymer in vinyl chloride polymerization.
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    Longitudinal acoustic modes in cycloalkanes (1981)
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    Polymer bulletin 5 (1981), S. 175-177 
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    Notes: Summary The longitudinal acoustic modes (LAM) of several cycloalkanes ((CH2)14 to (CH2)96) measured by Raman spectroscopy are described. The frequency differences between the LAMs of the cycloalkanes and the corresponding n-alkanes are explained by a simple linear chain model. It is shown that the LAM-modes are practically not affected by the gauche conformations of the two folds in the cyclic molecule.
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  • 92
    Electronic Resource
    Electronic Resource
    A continuum analysis of a system of many ‘real’ chains confined between a pair of ‘sticky’ surfaces, with application to the ‘sandwich’ model of bulk polymers (1981)
    Springer
    Polymer bulletin 5 (1981), S. 179-186 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary An analysis is made of a system of many interacting chains confined between a pair of surfaces which exert a short range attraction on the chains. The free energy of the system is determined from the partition functions of the confined chains which are, in turn, determined by solutions to the self consistent field form of the diffusion equation with mixed boundary conditions. The incorporation of the analysis into the ‘sandwich’ model of bulk polymers is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00265163
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  • 93
    Electronic Resource
    Electronic Resource
    Studies on syntheses and permeabilities of special polymer membranes (1981)
    Springer
    Polymer bulletin 5 (1981), S. 195-200 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The permeation and separation characteristics of methanol/n-pentanol systems and n-propanol/n-heptane systems through nylon 12 membranes were studied by changing the feed composition of the binary organic mixtures. These characteristics were discussed from the viewpoints of physical and chemical nature of the permeating molecules and the membrane.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00265165
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  • 94
    Electronic Resource
    Electronic Resource
    Preparation and study of terephthalate copolyester of ethylene glycol and butane-1,4-diol (1981)
    Springer
    Polymer bulletin 5 (1981), S. 187-194 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Random terephthalate copolyesters of ethylene glycol and butane-1,4-diol of various compositions were prepared by trans-esterification of poly(ethylene terephthalate) (PET) with butane-1,4-diol (BD). Proton nuclear magnetic resonance spectroscopy (NMR) was used to elucidate the structure and compositions of copolyesters. The thermal behaviour of the copolyesters were investigated by differential thermal analysis (DTA). Intrinsic viscosities were measured in orthochlorophenol at 30°C.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00265164
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  • 95
    Electronic Resource
    Electronic Resource
    Cationic modification of polystyrene (1981)
    Springer
    Polymer bulletin 5 (1981), S. 201-207 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper concerns the cationic modification of polystyrene by the electophilic substitution of polystyrene with S-methylthiocarbcxonium.The substitution is quantitative and gives poly p-(methylthio) carbonylstyrene. After hydrolysis and purification poly (p-carboxystyrene is obtained. The polymers are formed without degradation after this cationic modification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00265166
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  • 96
    Electronic Resource
    Electronic Resource
    13C NMR spin-lattice relaxation in solid poly(methyl methacrylate) (1981)
    Springer
    Polymer bulletin 5 (1981), S. 255-261 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary 13C spin-lattice relaxation rates R1 in samples of solid PMMA have been measured with CP MAS NMR. Isotactic, atactic, syndiotactic, and the 1∶2 i-s PMMA complex were measured, along with atactic samples containing bisdioxan or the monomer as a plasticizer. The reorientation of the α-methyl protons is the dominant relaxation source for the methylene, α-methyl and quarternary carbon nuclei. Increased mobility of the polymer in the presence of a plasticizer is not reflected in significant changes in R1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254711
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  • 97
    Electronic Resource
    Electronic Resource
    Effectiveness and limits of magnetic resonance techniques in the identification of different coordination pathways of the Mn(II) in the presence of biomacromolecules (1981)
    Springer
    Polymer bulletin 5 (1981), S. 263-269 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Magnetic resonance techniques yield important information on different coordination behaviour of Mn(II) in the presence of biomacromolecules. A preliminary study on model systems is necessary to have a deeper insight on dynamics and structural aspects. The EPR technique is not able to identify a binding interaction between Trp and manganous ion when the metal is bonded to the Imidazole. Proton shift NMR studies on the Mn(II)-5′ATP-Imid complex evidenziate a ternary system formation and a stacking interaction between the imidazole-ring and the nucleotide purine-moiety. An EPR and NMR combined analysis on the Mn(II)-5′ATP-Trp system points out a stacking interaction and the simultaneous presence of a covalent binding between the metal ion and the biomolecules. The role of the metal ion to favour this coordination is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254712
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  • 98
    Electronic Resource
    Electronic Resource
    Dynamical polymer coil overlap observed by NMR on polystyrene chains (1981)
    Springer
    Polymer bulletin 5 (1981), S. 277-284 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary It is shown that the transverse magnetic component of protons bound to polystyrene chains in solutions is sensitive to the slow chain diffusion through entanglements. A theoretical interpretation of the dynamical polymer coil overlap observed by NMR is proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254714
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  • 99
    Electronic Resource
    Electronic Resource
    NMR study of molecular motion in poly(ethylene oxide) (1981)
    Springer
    Polymer bulletin 5 (1981), S. 271-275 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Proton second moment and spin-lattice relaxation times T1, T1e and T1D for helical poly (ethylene oxide) 5000 over a wide temperature range are measured. The results of CW and pulse experiments corroborate the existence of a motional process in the crystalline region of the polymer interpreted as oscillation or rotation of molecules around their helical axes. The activation energy for this type of motion is found to be 12 kcal/mole.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254713
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  • 100
    Electronic Resource
    Electronic Resource
    Proton spin-lattice relaxation in thylakoid membranes of chloroplasts (1981)
    Springer
    Polymer bulletin 5 (1981), S. 285-289 
    Details
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Measurements of proton spin-lattice relaxation time T1 for thylakoid membranes of wheat chloroplast suspensions as a function of proton concentration in solvent are performed. The solvent was a mixture of H2O and D2O. Different contributions to the proton relaxation process due to dipolar interactions are considered. The dipolar interactions p-p′ and p-i between exchangeable protons /p/ of membrane of solvent and non-exchangeable ones of membrane /p′/ and paramagnetic ions /i/ give predominant contribution to the relaxation process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254715
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