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  • Springer  (88.334)
  • 1980-1984  (88.334)
  • 1940-1944
  • 1925-1929
  • 1982  (44.622)
  • 1981  (43.712)
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Verlag/Herausgeber
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  • 1980-1984  (88.334)
  • 1940-1944
  • 1925-1929
Jahr
  • 1
    Digitale Medien
    Digitale Medien
    Multibreath tracer species dynamics in the lung (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460935
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  • 2
    Digitale Medien
    Digitale Medien
    Global stability of population models (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460938
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  • 3
    Digitale Medien
    Digitale Medien
    The logistic equation with a diffusionally coupled delay (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459438
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  • 4
    Digitale Medien
    Digitale Medien
    Uncertainty in physiology and physics (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 141-149 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459439
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  • 5
    Digitale Medien
    Digitale Medien
    Consensusn-trees (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 239-244 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459446
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  • 6
    Digitale Medien
    Digitale Medien
    Morphogen pattern formation and development in growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 259-270 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462200
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  • 7
    Digitale Medien
    Digitale Medien
    Simulation experiments with a model for cellular growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 271-278 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462201
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  • 8
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462204
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  • 9
    Digitale Medien
    Digitale Medien
    On Zeeman's equations for the nerve impulse (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 279-325 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462202
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  • 10
    Digitale Medien
    Digitale Medien
    Asymptotic analysis of the Michaelis-Menten reaction equations (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 375-388 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459428
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  • 11
    Digitale Medien
    Digitale Medien
    Pulse evolution on coupled nerve fibres (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 389-400 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459429
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  • 12
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459430
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  • 13
    Digitale Medien
    Digitale Medien
    The construction of homogeneous nets (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 415-426 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459431
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  • 14
    Digitale Medien
    Digitale Medien
    Contractile analysis and kinetic energy of the myocardium (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459433
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  • 15
    Digitale Medien
    Digitale Medien
    Limit cycles in periodically perturbed population systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 463-485 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459434
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  • 16
    Digitale Medien
    Digitale Medien
    On a unified approach to pattern generation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 513-516 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459437
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  • 17
    Digitale Medien
    Digitale Medien
    An equivalence result for integral equations with application to branching processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 1-15 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459415
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  • 18
    Digitale Medien
    Digitale Medien
    General solution for flow and stress phenomena in elastic vessles (Navier-Stokes) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 29-42 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A method is developed for a full nonlinear evaluation of all velocities and stresses represented in the Navier-Stokes equations and in the general stress tensor. The information required is essentially that for solution of linearized forms. The solution is analytical except for the calculation of the axial velocity, which requires computer assistance to step through time and space. The treatment of the problem, although directed towards solutions involving fluid flow in elastic vessels, is also adaptable to solid deformations (strain vs rate of strain) where the general stress tensor applies. A special case for the distorting ellipse is presented as well as a limited, spatially analytic, solution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459417
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  • 19
    Digitale Medien
    Digitale Medien
    Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 43-56 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459418
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  • 20
    Digitale Medien
    Digitale Medien
    Stochastic compartmental models with banching and immigrant particles (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 75-86 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459420
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  • 21
    Digitale Medien
    Digitale Medien
    Mode analysis of physiological oscillators intercoupled via pure time delays (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 57-74 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The study of bi-directionally coupled oscillators is relevant in biological modelling of such systems as gastro-intestinal electrical activity, cardiac pacemarkers, cardiovascular and respiratory interactions and circadian rhythms. Interconnecting pathways in biological systems often exhibit pure time-delay characteristics. In this paper the multiple-mode limit-cycle behaviour of such systems is analysed using the method of harmonic blance. It is shown that the coupling time delay radically affects the number, frequency and amplitudes of entrained limit-cycles.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459419
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  • 22
    Digitale Medien
    Digitale Medien
    Bifurcation, stability diagrams, and varying diffusion coefficients in reaction-diffusion equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 87-102 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effect of keeping all the parameters constant, except the diffusion coefficients, in a pair of reaction-diffusion equations is studied. It is shown that the stability of the constant solution and the bifurcation points can be easily established by constructing a simple stability diagram. The possible qualitatively different diagrams are enumerated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459421
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  • 23
    Digitale Medien
    Digitale Medien
    Random ecological systems with structure: Stability-complexity relationship (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 103-117 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We have numerically examined more than one million Large Complex Systems (LCS) of interacting variables (interpretable as interacting populations) governed by Generalized Lotka-Volterra Equations (GLV), with self-regulation term. The scope was to have some insight on the stability-complexity relationship. We considered systems of prey-predator type, and we gave appropriate rules for constructing the model systems, rules that specify the behaviour of model systems in order to put them near the biological reality. The results show, among other things, a strict correlation between the stability and the prey-predator ratio (which, in our model, uniquely determines the connectedness of the system).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459422
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  • 24
    Digitale Medien
    Digitale Medien
    Remark on the article, “Applied catastrophe theory in the social and biological sciences” by M. A. B. Deakin (1980) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 149-150 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459425
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  • 25
    Digitale Medien
    Digitale Medien
    Transient effects on the initial rate of oxygenation of red blood cells (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 119-134 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The rate-controlling process in the oxygenation of red blood cells is investigated using a Roughton-like model for oxygen diffusion and reaction with hemoglobin. The mathematical equations describing the model are solved using two independent techniques, numerical inversions of the Laplace transform of the equations and numerical solutions via an implicit-explicit finite difference form of the equations. The model is used to re-examine previous theoretical models that incorporate either a red cell membrane that is resistive to oxygen diffusion or an unstirred layer of water surrounding the cell. Although both models have been postulated to be equivalent, the results of the computer simulations demonstrate significant differences between the two models in the rate of oxygenation of the red cells, depending upon the values chosen for the diffusion coefficient for O2 in the membrane and the thickness of the water layer. The difference is apparently due to differences in the induction and transient periods of the water layer model relative to the membrane model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459423
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  • 26
    Digitale Medien
    Digitale Medien
    Energy and biological evolution—II. The mathematical structure of equilibrium states (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 537-547 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We examine certain mathematical structures presented in Part I. The most important of these are the energy structures determined by the couple (ω×E, ψ) the space of causality defined by ψ-1(0) and the notion of collapsibility, i.e., the descent of a species from a higher to a lower equilibrium configuration as a result of energy loss.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459407
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  • 27
    Digitale Medien
    Digitale Medien
    A stochstic model for a two-compartment reversible system (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 557-570 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459409
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  • 28
    Digitale Medien
    Digitale Medien
    Effects of dispersion on stability of multispecies prey-predator systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 571-578 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The general multispecies prey-predator system with Gompertz's antisymmetric interactions is nonlinearly stable in the absence of dispersion and continues to remain stable with dispersion under both homogeneous reservoir and zero flux boundary conditions in a region containing the equilibrium state. It is proved that a general multispecies food-web model without antisymmetric interactions is stable in the absence of dispersion and remains stable with dispersion in the above-mentioned region.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459410
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  • 29
    Digitale Medien
    Digitale Medien
    Repeatability of experiments (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 593-593 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459413
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  • 30
    Digitale Medien
    Digitale Medien
    Graph theoretical criteria for stability and boundedness of predator-prey systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 579-585 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We introduce a graphical approach in the study of the qualitative behavior ofm species predator-prey systems. We prove that tree graphs imply global stability for Volterra models and local stability for general models; furthermore, we derive sufficient conditions so that loop graphs imply stability and boundedness of the solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459411
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  • 31
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    Digitale Medien
    A reply to “repeatability of experiments” by R. B. Campbell (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 594-595 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459414
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  • 32
    Digitale Medien
    Digitale Medien
    An epizootic model of an insect-fungal pathogen system (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 731-739 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A system of integro-differential equations is derived to describe epizootics of a fungal pathogen in an insect population. Because of piecewise continuous behavior under some parametric conditions, it is concluded that standard phase orbits can be misleading. Using a different analytic approach yields a simple system of finite difference equations. Both the continuous and discrete versions are compared to classical forms. The continuous version differs from a classical one in possessing a second derivative dependent on population density. The discrete version differs in maintaining positive, non-zero populations of both infectives and susceptibles in finite time.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462280
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  • 33
    Digitale Medien
    Digitale Medien
    On feedback control of gonadotropin secretion (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 741-748 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This note is an attempt to demonstrate that hypothalamic pulsatile GnRH secretion is not the result of a short-term, negative steroid hormone feedback. Clarification of this point is of importance for further modelling the control of gonads.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462281
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  • 34
    Digitale Medien
    Digitale Medien
    The development of largangians for biological models (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 749-760 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A modern theory of the calculus of variations is used to form necessary and sufficient conditions for the existence of a Lagrangian representation of a system of first-order ordinary differential equations. There exists a theorem to the effect that when a system of ordinary differential equations is variationally self-adjoint, the fulfillment of such conditions is guaranteed. In addition, self-adjointness, allows establishement of an algorithm by which a Lagrangian for the system may be explicitly constructed. Examples in mathematical biology are given to illustrate the use of the stated theorem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465178
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  • 35
    Digitale Medien
    Digitale Medien
    An optimal control model of diabetes mellitus (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 793-808 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Engineering optimal control theory is applied to equations describing insulin and glucose interactions. The nature of the optimal controller is established. It is shown how the results can be utilized in a closed loop feedback control system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465181
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  • 36
    Digitale Medien
    Digitale Medien
    Biological optimality: Comparison of generalized feasibility and optimality conditions for linear, error-minimizing systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 777-791 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An attempt is made to compare the conditions for the general error-optimality of linear systems developed by Kalman with the conditions for feasibility of linear models of neuromuscular and physiological control systems. Models of three actual physiological systems are tested for both the above criteria. Theoretical analysis presented here shows that there are no simple relationships between the two sets of conditions. Analysis carried out on the physiological systems models suggests the need for a general set of conditions for other optimality criteria, such as time and energy minimization, similar to Kalman's condition for error minimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465180
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  • 37
    Digitale Medien
    Digitale Medien
    The development of anoxia following occlusion (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 851-877 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465185
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  • 38
    Digitale Medien
    Digitale Medien
    Announcements (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 899-900 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465188
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  • 39
    Digitale Medien
    Digitale Medien
    Comparative performance of polynomial signal extraction (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 93-104 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A stochastic approximation problem for polynomic operators is formulated. The performance of polynomic operators of various degrees is compared. The effect of causality constraints is also examined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600036
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  • 40
    Digitale Medien
    Digitale Medien
    Feedback system design: The single-variate case — Part I (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 137-169 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A recently developed algebraic approach to the feedback system design problem is reviewed via the derivation of the theory in the single-variate case. This allows the simple algebraic nature of the theory to be brought to the fore while simultaneously minimizing the complexities of the presentation. Rather than simply giving a single solution to the prescribed design problem we endeavor to give a complete parameterization of the set of compensators which meet specifications. Although this might at first seem to complicate our theory it, in fact, opens the way for a sequential approach to the design problem in which one parameterizes the subset of those compensators which meet the second specification...etc. Specific problems investigated include feedback system stabilization, the tracking and disturbance rejection problem, robust design, transfer function design, pole placement, simultaneous stabilization, and stable stabilization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600050
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  • 41
    Digitale Medien
    Digitale Medien
    Editorial (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 267-268 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599010
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  • 42
    Digitale Medien
    Digitale Medien
    Rational approximation via selective modal analysis (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 433-445 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract We describe a recently developed framework for exploring the structure of linear time-invariant models of large systems, and for constructing interpretable or physically-based, reduced-order models that reproduce selected modes of the original systems to a desired accuracy. Application of this framework to constructing lumped approximations for interconnections of lumped and distributed systems is briefly explored.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599022
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  • 43
    Digitale Medien
    Digitale Medien
    Limits on the computing power of biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 59-67 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460939
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  • 44
    Digitale Medien
    Digitale Medien
    A topological study of the base sequences of MS2 and ϕX174 genoma (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 81-88 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460941
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  • 45
    Digitale Medien
    Digitale Medien
    Volume of the conducting airways calculated from morphometric parameters (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 101-109 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460943
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  • 46
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460944
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  • 47
    Digitale Medien
    Digitale Medien
    The diffusion transit time; A simple derivation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 89-99 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460942
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  • 48
    Digitale Medien
    Digitale Medien
    Nonlinear oscillations in biology (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 121-123 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460946
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  • 49
    Digitale Medien
    Digitale Medien
    A comment on Lin's paper on nonlinear diffusion in biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 117-120 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02460945
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  • 50
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459443
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  • 51
    Digitale Medien
    Digitale Medien
    Models on prebiotic polymer competition: A deterministic approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 213-232 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459444
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  • 52
    Digitale Medien
    Digitale Medien
    Extinction probabilities in microbial predation: A birth and death approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 165-181 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459441
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  • 53
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459445
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  • 54
    Digitale Medien
    Digitale Medien
    Spatially localized interactive neural populations—I. A mathematical model (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 427-446 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459432
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  • 55
    Digitale Medien
    Digitale Medien
    A one-compartment model with stochastic parameter (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 503-512 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459436
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  • 56
    Digitale Medien
    Digitale Medien
    A dose-response model for estimating lifetime tumor risks when cell killing occurs (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 487-501 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459435
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  • 57
    Digitale Medien
    Digitale Medien
    A stochastic model for then-compartment irreversible system (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 549-561 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462312
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  • 58
    Digitale Medien
    Digitale Medien
    Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 563-577 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462313
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  • 59
    Digitale Medien
    Digitale Medien
    Dynamic structure theory: A structural approach to social and biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 579-591 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462314
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  • 60
    Digitale Medien
    Digitale Medien
    Peak drug levels in linear pharmacokinetic systems—II. Conditions for a paradoxical injection rate effect with rectangular input (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 705-715 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458419
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  • 61
    Digitale Medien
    Digitale Medien
    Peak drug levels in linear pharmacokinetic systems—I. Effect of rate of injection (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 693-703 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458418
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  • 62
    Digitale Medien
    Digitale Medien
    Selection under random mutations in stochastic eigen model (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 17-28 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The concept of natural selection is examined, which is one of basic principles for the Darwinian interpretation of evolution. In this model selection is defined as a solution of the deterministic Eigen equation. Next, the random effect is introduced through the mutation term. However, the probability of finding the solution expressing the selection is shown to be smallest. The validity of the model and its applicability to polynucleotide replication are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459416
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  • 63
    Digitale Medien
    Digitale Medien
    Factors defining the rate of oxygen uptake by the red blood cell (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 135-147 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Using numerical methods, the initial rates of oxygen uptake by the red blood cell have been computed. The methods accommodate both a water layer and membrane which may act as diffusive impedance to gas influx. The differential solubilities of the gas in these two layers have also been incorporated in the methods. The presence of a 0.50–0.65 μm deoxygenated water layer has been calculated to simulate the experimental results by Roughton (1959). Experimental studies of CO and NO uptake by the red cell could also be simulated. Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell (Weingardenet al., submitted for publication), the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible. Using a thin layer-red cell oxygenation system, the rates of oxygenation were determined for red cells surrounded by a 4.2 μm deoxygenated water layer. The rates were found to compare favorably to the results of the theoretical model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459424
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  • 64
    Digitale Medien
    Digitale Medien
    Book review (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 151-151 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459426
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  • 65
    Digitale Medien
    Digitale Medien
    Role of the hypergeometric distribution in the transmission of excitation through sympathetic Ganglia (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 152-152 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459427
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  • 66
    Digitale Medien
    Digitale Medien
    On a class of finite deformations of elastic soft tissues (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 175-192 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Due to the complicated physiological structure of soft biological tissues, stresses can only be measured after the specimen has been stretched to many times of its related length. Therefore, the classical constitutive equations of finite elasticity developed for vulcanized, rubbery materials and the linear theories developed for most engineering materials cannot be applied to soft tissues which are highly elastic in nature. In this article, utilizing a mechanical model developed by Demiray for soft tissues, a class of finite deformations of some tissues is studied and the results are compared with experiment and the existing literature. These problems are the simultaneous extension and twisting of a circular cylindrical bar, the bending of a rectangular block, and the pure shear of a rectangular prism. It is believed that solutions to these problems may find some applications in plastic surgery.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463246
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  • 67
    Digitale Medien
    Digitale Medien
    Effects of convective and dispersive migration on the linear stability of a two species system with mutualistic interactions and functional response (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 271-282 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper, effects of convective and dispersive migration on the linear stability of the equilibrium state of a two species system with mutualistic interactions and functional response have been investigated. In both finite and semi-infinite habitats, it has been shown that the otherwise stable equilibrium state without dispersal remains so with dispersal also, both under flux and reservior conditions. In the case of finite habitat, the degree of stability increases as dispersal coefficients of the two species increase. The effect of convective migration also is to stabilize the equilibrium state in this case.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463251
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  • 68
    Digitale Medien
    Digitale Medien
    Announcements (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 307-307 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463253
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  • 69
    Digitale Medien
    Digitale Medien
    A model of the spatial-temporal characteristics of the alpha rhythm (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 283-305 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A linear spatially distributed model of a chain of neurons and interneurons was investigated in relation to the generation of propagated alpha rhythmic activity. It was assumed that the elements of the chain were interconnected by means of recurrent collaterals and inhibitory fibres in such a way that the connectivity functions were assumed to be homogeneous and their strength was an exponentially decreasing function of distance. It was found that such a neuronal chain shows propagation properties for frequencies in the alpha band. The results obtained with the model are in agreement with the phase velocities encountered experimentally. In this way, it was possible to estimate the length of the neural fibres responsible for the phenomenon of propagated activity. The estimates obtained are in good agreement with recent quantitative neuroanatomical data on the circuitry of the neocortex.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463252
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  • 70
    Digitale Medien
    Digitale Medien
    A behavioral summary for completely random nets (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 309-320 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper characterizes the cycle structure of a completely random net. Variables such as number of cycles of a specified length, number of cycles, number of cyclic states and length of cycle are studied. A square array of indicator variables enables conveninent study of moment structure. Additionally, exact and asymptotic distributional results are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462282
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  • 71
    Digitale Medien
    Digitale Medien
    Eigensolutions of nonlinear wave equations in one dimension (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 321-337 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A class of nonlinear equations describing the steady propagation of a disturbance on the infinite interval in one dimensional space are shown under certain conditions to admit solution with a unique velocity of propagation. The class of equations describe both initial and final homogeneous steady states which are asymptotically stable with respect to uniform perturbations, in contrast to the Fisher equation, which does not.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462283
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  • 72
    Digitale Medien
    Digitale Medien
    Comparison of models of insulin release (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 399-409 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model for insulin secretion with a storage and a labile compartment, as well as a provisionary factor, is combined with a signal model in which the signal can be the difference between an excitation and an inhibition, or the difference in concentrations inside and outside some cell components. The model, using a single set of values for the parameters, accounts in a semiquantitative manner for all of the regularly appearing features of the insulin secretion from thein vitro perfused pancreas to a wide range of patterns of glucose and tolbutamide stimulation. Among the features which can be accounted for are: early and late secretion of insulin as a function of glucose in terms of a single parameter; the apparent depletion and recovery during a pulsed pattern of stimulation by tolbutamide; the hypersecretion following a short period of rest during a prolonged stimulation by glucose; the negative spike which occurs when the concentration of glucose, which has been maintained for a period of time, is suddenly reduced to a lower level; and the appropriate responses to slow and fast ramp functions of glucose concentration.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462288
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  • 73
    Digitale Medien
    Digitale Medien
    Example of a system which is computation universal but not effectively programmable (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 443-447 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The incorporation of a chaotic component in a computing system is incompatible with its being effectively programmable. The example presented shows that concepts of programming suitable for biological systems may differ from those which have grown out of our experience with present day digital computers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462291
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  • 74
    Digitale Medien
    Digitale Medien
    Primary events in odour detection (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 411-423 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An analysis of the interaction between stimulus molecules and the olfactory receptor cell membrane is presented. The model is based upon a sequence of events, i.e. stimulus delivery at the olfactory epithelium, absorption of molecules in the mucus layer, diffusion of the molecules towards the receptor cells and molecule-receptor cell membrane interaction. The mathematical analysis considers the situation during electrophysiological experiments, where an odour puff is delivered at an exposed olfactory mucosa. Such a situation resembles sniffing of odour samples. The analysis is discussed in relation to experimental evidence.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462289
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  • 75
    Digitale Medien
    Digitale Medien
    Analytical model of hygroscopic particle behavior in human airways (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 425-442 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model is developed to calculate the deposition of hygroscopic aerosols in the human tracheobronchial (TB) tree. The TB airflow pattern assumed is consistent with experimental observations and accounts for anatomical features such as the larynx and cartilaginous rings in large airways. Some original deposition efficiency formulae are presented for laminar and turbulent airstreams. Stepwise growth is simulated by changes in particle size and density at each TB generation. The dose distribution of NaCl aerosols is studied as a function of inhaled particle size and flow rate. Two NaCl growth rate curves are used which differ in the mode of aerosol-air mixing in the trachea. The initial rate of aerosol mixing in the human due to the laryngeal jet is shown to be an important factor affecting the deposition of hygroscopic aerosols. Total TB deposition of NaCl exceeds that for nonhygroscopic particles of the same inhaled aerodynamic size. Hygroscopic growth can also influence the regional TB distribution of dose when submicron NaCl particles grow rapidly enough to deposit by impaction and sedimentation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462290
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  • 76
    Digitale Medien
    Digitale Medien
    Remark on the letter by Zhitomirsky and Kagna (1980) (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 449-449 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462292
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  • 77
    Digitale Medien
    Digitale Medien
    Announcements (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 451-452 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462294
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  • 78
    Digitale Medien
    Digitale Medien
    Mathematical model for the study of fertility and viability in inbreeding populations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 491-500 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Granted that a single or complex gene is responsible for inbreeding depression, theoretical expressions for fertility and viability are obtained in different diploid populations: brother-sister, half-brother-sister, cousins and double-cousins. The conclusions of the study of viability variations according to the coefficient of parentage are proved by the results of experiments and lead to a new view of genetic load.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459405
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  • 79
    Digitale Medien
    Digitale Medien
    Energy and biological evolution—I. The equilibrium states of biochemical processes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 501-535 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The Thom gradient model of morphogenesis poses the followinga posteriori problem: “From the observed morphology of a given natural process (effect) determine the dynamics of the process (cause)”. In this paper we consider the classicala priori problem: “Given the cause (dynamics) determine the effect (resultant morphology)”. We find that in biochemical processes the mechanisms for energy activation, energy-matter interaction and energy dissipation determine the dynamics. Furthermore there exists basic energy mechanisms which drive the equilibrium states through the elementary catastrophes of Thom. A comparison with current theories shows that our models describe open ecological food chains and their dynamical systems generalize the equations of organisation posed by M. Eigen.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459406
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  • 80
    Digitale Medien
    Digitale Medien
    Energy and biological evolution—III. Theoretical ecology and macromolecular self-organization (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 549-555 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We show that the elementary models of biochemical evolutionary processes are the bases for the study of open ecological systems and macromolecular self-organisation. We deduce a biochemical analogue for the basic closed phytoplankton-zooplankton food chain. The perturbation of the Michaelis-Menten mechanism which determines the nutrient-dependent growth rate of the phytoplankton species leads to higher catastrophes for the nutrient equilibrium manifold. The umbilic models are generalizations of the equations of organization of Eigen.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02459408
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  • 81
    Digitale Medien
    Digitale Medien
    Nonlinear generalizations of the Kedem-Katachalsky equations for ionic fluxes (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 761-775 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The transport equation of Kedem and Katchalsky for the flux of ions through a membrane is generalized to demonstrate explicitly the role of impermeant ions in determining its mathematical form. Whereas the Kedem-Katchalsky equation is linear in the salt concentrations in the bathing solutions, the more general equation is bilinear (and symmetric) in the ionic concentrations of the permeant species. The Kedem-Katchalsky flux equation is further generalized to include explicitly a term for ion-exchange in systems having more than a single permeant salt. This additional term is also bilinear (and antisymmetric) in the concentrations of the exchanging ionic species. Flux equations are derived for systems having (1) a single mono-monovalent salt, (2) two mono-monovalent salts and (3) an arbitrary number of salts with no restriction upon the valencies of the ionic components. Since it has no effect upon the form of concentration-dependent terms in the flux equations, coupling to volume flow is neglected.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465179
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  • 82
    Digitale Medien
    Digitale Medien
    Some applications of the concept of body forces for the myocardium (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 819-840 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical theory of the dynamics of the myocardium based on the concept of body forces is applied to account for two different experimental results. The first result consists of a relation between oxygen consumption and the kinetic energy of the myocardium. The second set of results provides a consistent interpretation of the relationship between different indices used to assess the ventricular performance.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465183
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  • 83
    Digitale Medien
    Digitale Medien
    On the stochastic theory of compartments: A semi-Markov approach for the analysis of theK-compartmental systems (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 809-817 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper a semi-Markov process approach is developed to analyse stochastic compartmental systems using straightforward probabilistic arguments. Explicit expressions for several characteristics of thek-compartmental systems with a Poisson process input are derived and various models found in the literature arising from biological applications are generalised here using the semi-Markov process technique.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465182
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  • 84
    Digitale Medien
    Digitale Medien
    Analysis of a nonlinear diffusion problem With Michaelis-Menten kinetics by an integral equation method (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 841-849 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model for oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics is analyzed by means of an intergral equation method. It is shown that an integral equation formulation can be used to obtain a numerical solution associated with this boundary and initial value problem. Through an illustrative numerical calculation we are able to obtain an accurate solution for both the steady and transient problems. Finally, a comparison is made with the numerical solution of McElwain and the variational solution of Anderson and Arthurs for the steady state and Lin's result concerning the unsteady state.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465184
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  • 85
    Digitale Medien
    Digitale Medien
    A note on exact solutions of two prey-predator equations (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 893-897 
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    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Exact solutions are obtained and discussed for classes of Lotka-Volterra and Leslie-Gower systems governing the interaction of two species. The classes are defined by certain constraints which are imposed on the time-dependent parameters of the equations. A general result for such systems is that each species is characterised by two time-scales: one representing natural growth and the other, the interdependence of the species.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465187
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  • 86
    Digitale Medien
    Digitale Medien
    Diffusion along intercellular spaces: An analysis of a transient situation (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 879-891 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We present an analysis of the diffusion of a tracer in a model of a cell-intercellular space system. The problem reduces to the resolution of a system of a linear partial differential equation and of a linear integral differential equation. The mathematical results have been obtained in terms of their Laplace transforms, which have been inverted by a numerical procedure for some parameter values. The importance of considering gradients of concentrations in intercellular spaces instead of lumping them with the external mediums has been discussed together with the possibility of extending Ussing's relation to transient cases, in order to detect active transports. Some possible implementations of the model to take into account more general situations have been considered.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02465186
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  • 87
    Digitale Medien
    Digitale Medien
    The asymptotic behavior of Hermite-Padé polynomials (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 305-309 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract We present speculations on the asymptotic behavior of Hermite-Padé polynomials of type I constructed from a set of functions with common branch points. The proposed form is consistent with all known results and numerical work.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599014
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  • 88
    Digitale Medien
    Digitale Medien
    Nested-feedback-loops realization of 2-D systems (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 321-343 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract Algorithms are derived for representation of double power series by branched continued fractions. Some properties of the branched continued fractions are given. Two new alternative structures for realization of a two-dimensional, zero memory nonlinear transfer characteristic are proposed. These structures permit the design of 2-D systems with relatively low sensitivity of the transfer function to coefficient errors. Generalized equivalence transformations of branched continued fractions are also presented. Illustrative examples are included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599016
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  • 89
    Digitale Medien
    Digitale Medien
    Port properties of nonlinear reciprocal networks (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 77-92 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract Time-invariantn-port networks are considered which are constructed from linear resistors and transformers, and nonlinear inductors and capacitors. A port property is sought which is analogous to the symmetry of the impedance matrix obtained in the linear case. Such a property is found using a stochastic characterization: with all resistors assumed to be at the one temperature and modelled to include the usual thermal noise, a fluctuating noise voltage will be observed at the ports of the networks. With some reasonable restrictions on the nature of the nonlinearities in the reactive elements, the vector of such noise voltages is shown to constitute what is known as a reversible stochastic process; in the linear case, reversibility holds if and only if the impedance matrix is symmetric.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600035
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  • 90
    Digitale Medien
    Digitale Medien
    Continuation algorithms for the eigenvalue problems (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 123-134 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract Three algorithms for the solution of the eigenvalue problem for a continuously parameterized family of sparse matrices are presented; a continuousLU (orLR) algorithm, a continuousQR algorithm, and a continuous Hessenberg algorithm. Each of the three algorithms may be implemented recursively and the sparsity of the given matrices is preserved throughout the numerical process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600038
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  • 91
    Digitale Medien
    Digitale Medien
    Stability analysis of complex dynamical systems (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 171-202 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract We present two new algorithms to estimate the domain of attraction of the equilibriumx=0 of a nonlinear systemx=f(x). One of these algorithms utilizes quadratic Lyapunov functions while the second algorithm makes use of norm Lyapunov functions. Both of these procedures yield estimates for the domain of attraction which are comparable to those obtained by existing methods; however, the present algorithms appear to be significantly more efficient than existing algorithms. We also show how sometimes the applicability of the above results can be extended to high order systems by invoking the comparison principle. In doing so, we establish some results for the comparison principle which are of interest in their own right. Specifically, we relate the domain of attraction of a low order comparison system to the domain of attraction of a higher order system and we give an interpretation of the comparison principle in terms of stability preserving maps. In order to demonstrate the applicability of the present results, and in order to compare the present results with existing results, several specific examples are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600051
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  • 92
    Digitale Medien
    Digitale Medien
    A block matrix representation of permutation networks (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 251-266 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract This work provides a mathematical framework for topologically-independent analysis of permutation networks. First, a structure-dependent representation is provided using matrices whose entries are switching expressions. Then, a transformation is presented which maps these matrices into structure-independent representations which are matrices whose entries are 0/1 matrices. Algebraic tools for manipulating the second type of matrices are also provided. Notions such as permutations realizable by a network, the rearrangeability property, and series and parallel connections of networks are defined and discussed with regard to the proposed representations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600055
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  • 93
    Digitale Medien
    Digitale Medien
    Toeplitz equations and Kronecker's algorithm (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 289-304 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A reliable algorithm, similar to the modifed Kronecker algorithm, is provided for the solution of the Polish polynomial approximation problem. Implicit in this solution is an efficient and reliable method for the algebraic solution of Toeplitz equations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599013
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  • 94
    Digitale Medien
    Digitale Medien
    Stieltjes series and soliton interaction (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 311-320 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract TheKdV andMkdV multisoliton solutions are found to be generated by rational Stieltjes functions of the non-linearity parameter, each pole of which can be associated with a soliton. The well-known asymptotic emergence of the separate solitons follows at once from the motion of the poles. Successive (n-1/n) Padé approximants to theN-soliton series are considered to show how the solitons are reconstructed from an increasing number of perturbation terms (n ≤N). Their asymptotic behaviour is particularly striking: as time increases the behaviour of then th approximation becomes that of an actualn-soliton solution, constituted by then leading solitons. Furthermore, it turns out that each such Padé approximation satisfies a conservation law: the mass of the approximated solution, equal to that of then solitons included, is conserved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599015
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  • 95
    Digitale Medien
    Digitale Medien
    A remark on the numerics of rational approximation and the rate of convergence of equally spaced interpolation of ¦x ¦ (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 367-377 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract In this note we review the technique for rational Chebyshev approximation as given by the generalization of the Remes algorithm and point out its connection to the generalized eigenvalue problem for symmetric Hankel matrices. By a classical example and some recent work it can be shown that interpolation with rational functions (even) on equidistant knots may lead to results that are superior to Chebyshev approximation by means of polynomials for comparable numerical work.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599018
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  • 96
    Digitale Medien
    Digitale Medien
    Optimal Hankel-norm approximation of continuous-time linear systems (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 407-431 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract A problem on optimal approximation of continuous-time linear systems is studied. The performance measure (error) is chosen to be the spectral norm of the difference between the Hankel operators associated with the original system and the approximant. It is shown that the Hankel operators associated with continuous-time systems and the Hankel matrices associated with discrete-time systems are related by an interesting correspondence property via bilinear transforms. This fact is then used to derive the continuous-time results (theory and algorithms) from the established discrete-time ones. Some simple examples are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599021
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  • 97
    Digitale Medien
    Digitale Medien
    Scattering theory and matrix orthogonal polynomials on the real line (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 471-495 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract The techniques of scattering and inverse scattering theory are used to investigate the properties of matrix orthogonal polynomials. The discrete matrix analog of the Jost function is introduced and its properties investigated. The matrix distribution function with respect to which the polynomials are orthonormal is constructed. The discrete matrix analog of the Marchenko equation is derived and used to obtain further results on the matrix Jost function and the distribution function.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01599024
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  • 98
    Digitale Medien
    Digitale Medien
    An efficient large systems analysis method using system dynamic behavior (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 57-76 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract This paper presents our unified approach to the solution of large system analysis problems. The macromodular behavioral technique combines multiple-logic function macromodeling, functional latency and nested macromodel. We take advantage of the dynamic behavior and the repetitive modular structure of a system to improve the computational efficiency during system analysis. Several Bipolar and MOSFET electronic networks are used to demonstrate the merits of the macromodular behavioral method for large system analysis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600034
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  • 99
    Digitale Medien
    Digitale Medien
    Design of FIR digital filters using tapped cascaded FIR Subfilters (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 43-56 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract This paper considers the design of an FIR digital filter by interconnecting a number of identical FIR subfilters with the aid of a few additional multipliers and adders. The overall structure is in the form of a tapped cascaded FIR subfilters. A composite method to determine the tapping coefficients along with the coefficients of the subfilter to approximate overall frequency response characteristic is proposed. Several numerical examples illustrating the proposed method are included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600033
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  • 100
    Digitale Medien
    Digitale Medien
    A general theory of broadband matching of an active load (1982)
    Springer
    Circuits, systems and signal processing 1 (1982), S. 105-122 
    Details
    ISSN: 1531-5878
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik
    Notizen: Abstract Given a passive frequency-dependent source impedance and an active or passive load and a preassigned transducer power-gain characteristic, necessary and sufficient conditions are given for the existence of a lossless reciprocal equalizer which, when operating between the given source and the given load, yields the desired transducer power-gain characteristic. The significance of the present approach is that the realization of the equalizer involves only driving-point synthesis by the Darlington theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01600037
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