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  • Springer  (43,712)
  • Springer Science + Business Media
  • 1980-1984  (43,712)
  • 1981  (43,712)
  • 1
    Electronic Resource
    Electronic Resource
    Multibreath tracer species dynamics in the lung (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460935
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  • 2
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    Global stability of population models (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460938
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  • 3
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    The logistic equation with a diffusionally coupled delay (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459438
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  • 4
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    Uncertainty in physiology and physics (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 141-149 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459439
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  • 5
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    Consensusn-trees (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 239-244 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459446
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  • 6
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    Morphogen pattern formation and development in growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 259-270 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462200
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  • 7
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    Simulation experiments with a model for cellular growth (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 271-278 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
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    URL: http://dx.doi.org/10.1007/BF02462201
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  • 8
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    Complementary extremum principles for a nonlinear model of heat conduction in the human head (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 341-346 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462204
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  • 9
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    On Zeeman's equations for the nerve impulse (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 279-325 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
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    URL: http://dx.doi.org/10.1007/BF02462202
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  • 10
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    Asymptotic analysis of the Michaelis-Menten reaction equations (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 375-388 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
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    URL: http://dx.doi.org/10.1007/BF02459428
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  • 11
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    Pulse evolution on coupled nerve fibres (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 389-400 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
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    URL: http://dx.doi.org/10.1007/BF02459429
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  • 12
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    Field-induced forces at dielectric interfaces as a possible mechanism of RF hearing effects (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 401-413 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
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    URL: http://dx.doi.org/10.1007/BF02459430
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  • 13
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    The construction of homogeneous nets (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 415-426 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
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    URL: http://dx.doi.org/10.1007/BF02459431
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  • 14
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    Contractile analysis and kinetic energy of the myocardium (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
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    URL: http://dx.doi.org/10.1007/BF02459433
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  • 15
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    Limit cycles in periodically perturbed population systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 463-485 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
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    URL: http://dx.doi.org/10.1007/BF02459434
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  • 16
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    On a unified approach to pattern generation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 513-516 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02459437
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  • 17
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    Limits on the computing power of biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 59-67 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.
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    URL: http://dx.doi.org/10.1007/BF02460939
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  • 18
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    A topological study of the base sequences of MS2 and ϕX174 genoma (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 81-88 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.
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    URL: http://dx.doi.org/10.1007/BF02460941
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  • 19
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    Volume of the conducting airways calculated from morphometric parameters (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 101-109 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460943
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  • 20
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    Variability in a single compartment system: A note on S. R. Bernard's model (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 111-116 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
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    URL: http://dx.doi.org/10.1007/BF02460944
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  • 21
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    The diffusion transit time; A simple derivation (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 89-99 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.
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    URL: http://dx.doi.org/10.1007/BF02460942
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  • 22
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    Nonlinear oscillations in biology (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 121-123 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460946
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  • 23
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    A comment on Lin's paper on nonlinear diffusion in biological systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 117-120 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460945
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  • 24
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    On the stochastic theory of compartments: The leaving process of the two-compartment systems (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 201-211 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.
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    URL: http://dx.doi.org/10.1007/BF02459443
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  • 25
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    Models on prebiotic polymer competition: A deterministic approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 213-232 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.
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  • 26
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    Extinction probabilities in microbial predation: A birth and death approach (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 165-181 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.
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  • 27
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    Prediction of the effect of the choroidal circulation on the retinal temperature during illumination (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 233-238 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.
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    URL: http://dx.doi.org/10.1007/BF02459445
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  • 28
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    Spatially localized interactive neural populations—I. A mathematical model (1981)
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    Bulletin of mathematical biology 43 (1981), S. 427-446 
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    ISSN: 1522-9602
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    Notes: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.
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  • 29
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    A one-compartment model with stochastic parameter (1981)
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    Bulletin of mathematical biology 43 (1981), S. 503-512 
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    Notes: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.
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    A dose-response model for estimating lifetime tumor risks when cell killing occurs (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 487-501 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.
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    URL: http://dx.doi.org/10.1007/BF02459435
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    A stochastic model for then-compartment irreversible system (1981)
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    Bulletin of mathematical biology 43 (1981), S. 549-561 
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    Notes: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.
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    URL: http://dx.doi.org/10.1007/BF02462312
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  • 32
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    Pulsatile blood flow in a rigid pulmonary alveolar sheet with porous walls (1981)
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    Bulletin of mathematical biology 43 (1981), S. 563-577 
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    Notes: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.
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    Dynamic structure theory: A structural approach to social and biological systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 579-591 
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    Notes: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
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    Peak drug levels in linear pharmacokinetic systems—II. Conditions for a paradoxical injection rate effect with rectangular input (1981)
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    Bulletin of mathematical biology 43 (1981), S. 705-715 
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    Notes: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.
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    Peak drug levels in linear pharmacokinetic systems—I. Effect of rate of injection (1981)
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    Bulletin of mathematical biology 43 (1981), S. 693-703 
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    Notes: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.
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    On a two urn model of Polya-type (1981)
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    Bulletin of mathematical biology 43 (1981), S. 33-45 
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    Notes: Abstract A two urn Polya-type scheme is considered in whichr black balls (corresponding to the stable form of an element) are added to urn one at every stage and the same number of balls are removed at random at every stage from the same urn. In between these two operations, which form a stage or iteration, a fixed number of balls is exchanged at random between urns one and two. Urn one has a given initial number of white balls (corresponding to a radioactive form of the same element). The problem of interest is to study the stochastic aspect of the number of white balls remaining in urn one (and/or urn two) aftern iterations.
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    Nonlinear biological oscillators: Action-angle variable approach with an application to Cowan's model of neuroelectric activity (1981)
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    Bulletin of mathematical biology 43 (1981), S. 21-32 
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    Notes: Abstract We obtain within the action-angle variable approach new expressions, involving the Dirac delta function, for time periods and time averages of dynamical variables which are useful for nonlinear biological oscillator problems. We combine these with Laplace transformation techniques for evaluating the required perturbation expansions. The radii of convergence of these series are determined through a complex variable approach. The method is powerful enough to yield explicit results for such systems as the two species Volterra model, Goodwin's model of protein synthesis etc. and as an illustration, is applied here to Cowan's model of neuroelectric activity. We also point out the usefulness of the action integral in the case where parameters occurring in dynamics have slow time variations.
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    A generalized Fokker-Planck equation in the case of the Volterra model (1981)
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    Bulletin of mathematical biology 43 (1981), S. 69-79 
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    Notes: Abstract Zwanzig and Mori's projection-operator method is used in order to derive a generalized nonlinear Fokker-Planck equation for one “relevant” species in the many species conservative Volterra model. The deterministic, autonomous, Markovian equations of motion, when averaged over a suitable ensemble of initial conditions in general give rise to a non-autonomous, non-Markovian stochastic process for the evolution of this relevant species. Moreover, this relevant species may show irreversible damping, although self-interaction terms are absent in the many species model.
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    A hydrodynamical study of the flow in renal tubules (1981)
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    Bulletin of mathematical biology 43 (1981), S. 151-163 
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    Notes: Abstract The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.
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    Some comments on the conductance of slow inward current in cardiac muscle (1981)
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    Bulletin of mathematical biology 43 (1981), S. 183-199 
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    Notes: Abstract Voltage clamp experiments, which determine the kinetic parameters of calcium conductance of cardiac muscle, (d ∞,f ∞, τ d and τ f ) are analyzed with a generally accepted expression for slow inward currentI s=g sdf (E-E R). Activation (d) and inactivation (f) reach the final valuesd ∞ andf ∞ with time constants τ d and τ f respectively. The analysis indicates that the measuredf ∞ agrees with the theoreticalf ∞, but the measuredd ∞ differs from the theoreticald ∞ by a factor which depends on τ d . The peak tension can be made to correlate closely with the theoreticald ∞ after a correction factor is applied to the raw measurements of activation. It can be shown that experiments designed to measure τ f can also be used to determine τ d with greater accuracy.
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    On the relevance of stochastic compartmental models to pharmacokinetic systems (1981)
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    Bulletin of mathematical biology 43 (1981), S. 245-247 
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    Identification of silent infections in SIR epidemics (1981)
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    Bulletin of mathematical biology 43 (1981), S. 249-257 
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    Notes: Abstract A deterministic model for an SIR epidemic with silent infections is investigated. It is shown for the model studied that the extent to which silent infections are present may be determined from data concerning only those individuals with symptomatic infection.
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    A reinforcement-depletion urn problem—I. Basic theory (1981)
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    Bulletin of mathematical biology 43 (1981), S. 327-340 
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    Notes: Abstract An urn contains balls of different colors. Specified numbers of each color are added and form a reinforcement. The total reinforcement is randomly removed, forming a depletion. The process, not necessarily with the same reinforcements, is performed a number of times. The factorial moment generating function of the urn configurations at any stage is given in terms of multivariate difference operators. Cases when the reinforcement vector is defined as a stochastic variable are considered. The problem is a generalization of an urn model associated with radioactive atoms and stable atoms proposed by S. R. Bernard. The solutions given here have a definite application to the problem of modelling tracers in compartmental systems.
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    Stochastic compartmental model with branching particles (1981)
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    Bulletin of mathematical biology 43 (1981), S. 347-360 
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    Notes: Abstract A multi-compartmental model with particles producing offspring according to the Markov branching process has been studied. Explicit results are given for the two-compartmental system and for irreversible general multicompartmental systems. The known models in stochastic compartmental analysis are shown to be particular cases of this model and applications are cited.
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    On Wei's fundamental equation for nerve excitation (1981)
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    Bulletin of mathematical biology 43 (1981), S. 371-372 
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    Phase-plane analyses of the Michaelis-Menten reaction equations (1981)
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    Bulletin of mathematical biology 43 (1981), S. 361-370 
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    Notes: Abstract The irreversible Michaelis-Menten scheme may be reduced to a pair of autonomous first-order differential equations. The phase-plane behaviour of these is investigated.
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    Reply to Chyuan-Yih Lee (1981)
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    Bulletin of mathematical biology 43 (1981), S. 372-373 
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    Further considerations in a theoretical description of gas transport in lung airways (1981)
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    Bulletin of mathematical biology 43 (1981), S. 517-548 
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    Notes: Abstract A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe〈1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O2 concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.
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    Effects of convective and dispersive interactions on the stability of two species (1981)
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    Bulletin of mathematical biology 43 (1981), S. 593-610 
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    Notes: Abstract The evolution and local stability of a system of two interacting species in a finite two-dimensional habitat is investigated by taking into account the effects of self- and cross-dispersion and convection of the species. In absence of cross-dispersion, an equilibrium state which is stable without dispersion is always stable with dispersion provided that the dispersion coefficients of the two species are equal. However, when the dispersion coefficients of the two species are different, the possibility of self-dispersive instability arises. It is also pointed out that the cross-dispersion of species may lead to stability or instability depending upon the nature and the magnitude of the cross-dispersive interactions in comparison to the self-dispersive interactions. The self-convective movement of species increases the stability of the equilibrium state and can stabilize an otherwise unstable equilibrium state. The effect of cross-convection (in absence of self-dispersion and self-convection) is to stabilize the equilibrium state in a prey-predator model with positive cross-dispersion coefficients for the prey species. Finally, it is shown that if the system is stable under homogeneous boundary conditions it remains so under non-homogeneous boundary conditions.
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    Role of the hypergeometric distribution in the transmission of excitation through sympathetic ganglia (1981)
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    Bulletin of mathematical biology 43 (1981), S. 611-618 
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    Notes: Abstract Various observations suggest that sympathetic ganglia act as local integrative centers redistributing preganglionic excitation (i.e. the information issued by the central nervous system) to the postganglionic fibers (and effector organs). In order to support this concept a simple mathematical model of the elementary integration process, treating the case of a single preganglionic compound action potential, has been developed. This quantitative description, based on a few elementary assumptions, shows a possible way of processing preganglionic excitation in the ganglion. It is shown that on a particular ganglion cell the probability distribution of the number of activated synapses obeys hypergeometric distribution and hence, the postganglionic compound action potential is built up of several compound action potentials occurring at different times. The former correspond to different groups of firing cells. The model discloses modes of structural and temporal pattern generation performed by the sympathetic ganglion.
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    The uniqueness of protein sequences: A Monte Carlo analysis (1981)
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    Bulletin of mathematical biology 43 (1981), S. 619-639 
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    Notes: Abstract Amino acid sequences have already been examined in some detail in order to relate them to structural aspects, homology and gene duplication. This report introduces the concept of internal uniqueness of tripeptides within protein sequences and uses the Monte Carlo method to study this property. Some idea of internal uniqueness may be obtained from such an analysis using only a single sequence if the probability of the random occurrence is about 0.001 or less. This method of analysis is similar to that used in quantitative evaluations of homology. When the probability of the random occurrence is larger than 0.001 a homologous group of sequences is required and the random probabilities may be compared with the real occurrences within the group. From such an examination insulin and cytochrome c are identified as protein sequences with high internal uniqueness. A comparison of data from internal uniqueness and gene duplication analyses shows that these two properties need not be related. Results of the analysis point to internal uniqueness as an additional parameter for inclusion in speculations on why twenty amino acids are coded in protein structure.
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    Tolerance nets (1981)
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    Bulletin of mathematical biology 43 (1981), S. 641-650 
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    Notes: Abstract The concept of a tolerance net formalises simultaneously spatial closeness and nearness of neuronal activity. A method of constructing tolerance group nets is presented, leading to a means of construction of all very homogenous tolerance nets as group quotients. The dihedral group of order eight is taken as an illustrative example.
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    Relation between diameter and flow in branches of the bronchial tree (1981)
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    Bulletin of mathematical biology 43 (1981), S. 681-691 
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    Notes: Abstract Two methods are described for calculating the value of the exponentx in the equation flow =k×diameter x , as pertaining to a branch of the bronchial tree. In the lungs from three humans, two dogs, one hamster, and one rat mean values ofx between 2.419 and 2.903 were found. They lie within the range of 2.333 to 3.0 predicted by the analysis of Uylings (Bull. Math. Biol. 39, 501–519, 1977).
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    Stochastic analysis of a nonlinear model for selection of biological macromolecules (1981)
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    Bulletin of mathematical biology 43 (1981), S. 665-680 
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    Notes: Abstract A stochastic analysis of a nonlinear selection model is presented. The model, based on Eigen and Schuster's theory of selection and evolution of biological macromolecules, considers the effects of fluctuations on the individual concentrations of macromolecules as well as the total population numbers in constrained systems. Our analysis shows that one of the models most often treated deterministically (referred to as constant organization in the literature) becomes unstable when fluctuations in the total population number are considered. An alternative model which apparently has built in self-regulating properties is analyzed and proves to be stable except for some special cases of degeneracy.
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    Compartmental models with multiple sources of stochastic variability: The one-compartment models with clustering (1981)
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    Bulletin of mathematical biology 43 (1981), S. 651-664 
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    Notes: Abstract Previous compartmental models have introduced variability either at the particle or at the replicate level. This paper integrates both types of variability through the concept of clustering. The paper develops two different, general clustered models, each with time-dependent hazard rates for the clusters and for the particles within the clusters, and each with random initial number and sizes of clusters. The coefficient of variation of the total number of particles,CV[X(t)], for either model is shown to be bounded below, under very broad conditions, by the coefficient of variation of the initial number of clusters,CV[c(0)]. This high relative variability of the clustered models makes them potentially very useful in kinetic modeling. In many applications, binding and clustering are common phenomena, and two applications of the models to such phenomena are breifly outlined.
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    Some trees are not interval graphs (1981)
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    Bulletin of mathematical biology 43 (1981), S. 717-717 
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    Annual Meeting of the Cell Kinetics Society (1981)
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    Bulletin of mathematical biology 43 (1981), S. 719-719 
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    IV. Referate (1981)
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    European journal of wildlife research 27 (1981), S. 220-220 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Seroepidemiologische Untersuchungen zum Vorkommen von Leptospirosen bei Schalenwild in der Bundesrepublik Deutschland (1981)
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    European journal of wildlife research 27 (1981), S. 283-287 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary 399 serum samples collected from native cloven-hoofed game were investigated by means of agglutinating-lysis reaction for antibodies against leptospirosis. Antibodies were found in 1,8 % of 169 sera from roe deer(Capreolus capreolus), in 2,1 % of 96 sera from red deer(Cervus elaphus) and in 18,6 % of sera from wild boars(Sus scrofa) in a serum dilution of 1:400 and higher. In 5,7 % of sera from 35 fallow deer(Dama dama) were only found suspicious titers (1:200). In 29 sera of mouflon(Ovis musimon) antibodies against leptospirosis were not detected. The most reactions were found againstL. icterohaemorrhagiae (31,7 %),L. ballum (17,1 %) andL. grippotyphosa (12,2 %). The significance of the serological findings is discussed.
    Abstract: Résumé 399 échantillons de sérum de 5 espèces d'Ongulés-gibier indigènes ont été analysés au moyen de la réaction d'agglutination quant à la présence d'anticorps contre les Leptospires. Dans 1,8 % des sérums de 169 chevreuils(Capreolus capreolus), dans 2,1 % des sérums de 96 cerfs(Cervus elaphus) et dans 18,6 % des sérums de 70 sangliers(Sus scrofa) le titrage s'avéra positif (1:400 et plus). 5,7 % des échantillons de sérum de 35 daims(Dama dama) révélèrent des teneurs suspectes (1:200), tandis que dans 29 échantillons de sérums de mouflons(Ovis musimon), aucun anticorps contre les leptospires n'a été décelé. Le plus souvent, les sérums réagissaient auxL. icterohaemorrhagiae (31,7 %),L. ballum (17,1 %) etL. grippotyphosa (12,2 %). La portée des constatations sérologiques fait l'objet d'une discussion.
    Notes: Zusammenfassung 399 Serumproben von 5 einheimischen Schalenwildarten wurden mittels Agglutination-Lysis-Reaktion auf das Vorhandensein von Antikörpern gegen Leptospiren untersucht. In 1,8 % der Seren von 169 Stück Rehwild(Capreolus capreolus), in 2,1 % der Seren von 96 Stück Rotwild(Cervus elaphus) und in 18,6 % der Seren von 70 Stück Schwarzwild(Sus scrofa) wurden positive Titer (1:400 und höher) gefunden. 5,7 % der Serumproben von 35 Stück Damwild(Dama dama) wiesen verdächtige Titer (1:200) auf, während in 29 Serumproben von Muffelwild(Ovis musimon) keine Antikörper gegen Leptospiren nachgewiesen wurden. Am häufigsten reagierten die Seren gegenL. icterohaemorrhagiae (31,7 %),L. ballum (17,1 %) undL. grippotyphosa (12,2 %). Die Bedeutung der serologischen Befunde wird diskutiert.
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    Rosenmißbildung bei einem Rehgehörn (1981)
    Springer
    European journal of wildlife research 27 (1981), S. 287-291 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The suspicion of a formation of a double rose in a roe head from the Minden-Lübbecke District in Nordrhein-Westfalen is taken as the occasion to discuss the phenomenom of double rose formation as described in the literature. The bulkiness and disorganised growth of the rose is seen as the chief characteristic of the head from the Minden-Lübbecke District. The cause of the malformation similar to a double rose is taken to be a disturbance of the hormones which affected the rose formation and then later faded away, so that the head was able to mature and be frayed largely in the normal way.
    Abstract: Résumé La présomption d'avoir à faire à une formation de meules superposées chez un bois de Chevreuil originaire du district de Minden-Lübbecke en Rhénanie-Westphalie est à l'origine d'une recherche bibliographique sur le phénomène. La caractéristique principale du bois du district de Minden-Lübbecke est la masse et le développement désordonné de ses meules. On admet que la cause de cette formation de meules superposées réside dans un déséquilibre hormonal passager ayant provoqué la malformation des meule, sans empêcher pour autant la maturation ultérieure du bois de telle sorte qu'il a pu être frayé normalement.
    Notes: Zusammenfassung Der Verdacht einer Doppelrosenbildung bei einem aus dem Kreis Minden-Lübbecke in Nordrhein-Westfalen stammenden Rehgehörn wird zum Anlaß genommen, das Phänomen der Doppelrosenbildung nach der Literatur abzuhandeln. Für das Gehörn aus dem Kreis Minden-Lübbecke wird als Hauptcharakteristikum die Massigkeit, das unorganisierte Wachstum der Rose gesehen. Als Ursache für die doppelrosenähnliche Mißbildung wird eine hormonelle Störung angenommen, die sich auf die Rosenbildung auswirkte, später abklang, so daß das Gehörn ausreifen und weitgehend normal gefegt werden konnte.
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    Dr. Heribert Kalchreuter Leiter des Fachgebietes „Wild- und Jagdökologie“ in der Bundesforschungsanstalt für Naturschutz und Landschaftsökologie (1981)
    Springer
    European journal of wildlife research 27 (1981), S. 293-294 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    On the number of solutions to a class of complementarity problems (1981)
    Springer
    Mathematical programming 21 (1981), S. 190-203 
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    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Cones ; Topological Degree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the problem of establishing the number of solutions to the complementarity problem. For the case when the Jacobian of the mapping has all principal minors negative, and satisfies a condition at infinity, we prove that the problem has either 0, 1, 2 or 3 solutions. We also show that when the Jacobian has all principal minors positive, and satisfies a condition at infinity, the problem has a unique solution.
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    Finding simplicial subdivisions of polytopes (1981)
    Springer
    Mathematical programming 21 (1981), S. 233-234 
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    ISSN: 1436-4646
    Keywords: Polytope ; Subdivision ; Simplex ; Volume ; Centroid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Subdivisions of polytopes are described which place any chosen vertex in a (near-) minimal number of simplices. Ancillary procedures to find volumes and centroids of polytopes are indicated.
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    Direct theorems in semi-infinite convex programming (1981)
    Springer
    Mathematical programming 21 (1981), S. 301-318 
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    ISSN: 1436-4646
    Keywords: Semi-infinite Programs ; Open Helly-type Theorems ; Finite Subprograms ; Convex Programs ; Multi-criteria Programs ; Quasi-convex Programs ; Quasi-differentiable Programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a semi-infinite quasi-convex program with certain regularity conditions possesses finitely constrained subprograms with the same optimal value. This result is applied to various problems.
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    A statistical estimate of the structure of multi-extremal problems (1981)
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    Mathematical programming 21 (1981), S. 348-356 
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    ISSN: 1436-4646
    Keywords: Multi-extremal Optimization ; Multinomial Distribution ; Bayes Estimate ; Monte Carlo
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The solution of ak-extremal problem is defined as the set of pairs (x i * , θi),i = 1, ⋯ ,k, where x t * isi th local minimum andθ i is the volume of the set of attraction of this minimum. A Bayesian estimate ofk and (θ 1 , ⋯ , θ k ) is constructed.
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    Symposium on network flows (1981)
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    Mathematical programming 21 (1981), S. 120-120 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    On solving a primal geometric program by partial dual optimization (1981)
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    Mathematical programming 21 (1981), S. 319-330 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Geometric Programming ; Duality Theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The several published methods for mapping a dual solution estimate to a primal solution estimate in posynomial geometric programming provide no criteria for deciding how much deviation from primal feasibility, or discrepancy between the primal and dual objective function values, should be permitted before the primal solution estimate is accepted by the designer. This paper presents a new and simple dual-to-primal conversion method that uses the cost coefficients to provide a sound economic criterion for determining when to accept a primal solution estimate. The primal solution estimate generated is the exact solution to a modified primal obtained from the given primal by modifying the cost coefficients, with the exponent matrix left unchanged. The method is shown to have desirable properties when coupled with a convergent dual algorithm.
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    Minimum cost spanning tree games (1981)
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    Mathematical programming 21 (1981), S. 1-18 
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    ISSN: 1436-4646
    Keywords: Game Theory ; Cost Allocation ; Spanning Tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.
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    Institute on deterministic and stochastic scheduling (1981)
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    Mathematical programming 21 (1981), S. 119-119 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    Polynomial algorithms for a class of linear programs (1981)
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    Mathematical programming 21 (1981), S. 121-136 
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    ISSN: 1436-4646
    Keywords: Linear Programming ; Polynomial Algorithms ; Total Unimodularity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes several algorithms for solution of linear programs. The algorithms are polynomial when the problem data satisfy certain conditions.
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    An algorithm for computing equilibria in a linear monetary economy (1981)
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    Mathematical programming 21 (1981), S. 182-189 
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    ISSN: 1436-4646
    Keywords: Equilibrium ; Linear Monetary Economy ; Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An algorithm is presented for computing equilibria in a linear monetary economy, that is, an exchange economy in which all individuals have linear utility functions and in which goods are bought and sold only in exchange for money. The algorithm computes the equilibrium prices by solving a finite sequence of linear programming problems.
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    Comment on a paper by M.C. Cheng (1981)
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    Mathematical programming 21 (1981), S. 229-232 
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    ISSN: 1436-4646
    Keywords: Primal Feasible Basis ; Dual Feasible Basis ; Basic Variable ; Nonbasic Variable ; Optimal Basic Solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In a recent paper M.C. Cheng proposed new criteria for the simplex algorithm which guarantee that (i) a nonbasic variable of a basic feasible solution will remain nonbasic in an optimal basic solution, (ii) a basic variable of a basic solution will remain basic in an optimal basic solution. This comment gives (i) a slight generalization of the first result and (ii) a counterexample to the second proposition.
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    Euro V — tims XXV (1981)
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    Mathematical programming 21 (1981), S. 240-240 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    An elementary survey of general duality theory in mathematical programming (1981)
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    Mathematical programming 21 (1981), S. 241-261 
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    ISSN: 1436-4646
    Keywords: Dual problem ; Duality Theory ; Optimality Conditions ; Price Functions ; Nonlinear Programming ; Integer Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We survey some recent developments in duality theory with the idea of explaining and unifying certain basic duality results in both nonlinear and integer programming. The idea of replacing dual variables (prices) by price functions, suggested by Everett and developed by Gould, is coupled with an appropriate dual problem with the consequence that many of the results resemble those used in linear programming. The dual problem adopted has a (traditional) economic interpretation and dual feasibility then provides a simple alternative to concepts such as conjugate functions or subdifferentials used in the study of optimality. In addition we attempt to make precise the relationship between primal, dual and saddlepoint results in both the traditional Lagrangean and the more general duality theories and to see the implications of passing from prices to price functions. Finally, and perhaps surprisingly, it appears that all the standard algorithms terminate by constructing primal and dual feasible solutions of equal value, i.e., by satisfying generalised optimality conditions.
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    International symposium on the occasion of the 25th anniversary of the econometric institute, rotterdam (1981)
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    Mathematical programming 21 (1981), S. 358-358 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    Monotone Einschließung durch Verfahren vom Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungsbegriffes (1981)
    Springer
    Computing 26 (1981), S. 33-44 
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    ISSN: 1436-5057
    Keywords: 65 J ; 65 H
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary A generalization of the concept of a divided difference operator introduced by J. W. Schmidt is derived. The inclusion of solutions by certain Regula-falsi-methods realized by a well known approximation of the Jacobian matrix, which is no divided difference operator in the sense of Schmidt but a realization of this generalization, is proved.
    Notes: Zusammenfassung Durch Verallgemeinerung des von J. W. Schmidt eingeführten Steigungsbegriffes gelingt es, bei Durchführung gewisser Verfahren vom Regula-falsi-Typ mit einer naheliegenden und häufig verwendeten Approximation der Funktionalmatrix, die keine Steigung im herkömmlichen Sinne darstellt, jedoch eine Realisierung der oben genannten Verallgemeinerung liefert, Einschließungsaussagen für Lösungen von Operatorgleichungen nachzuweisen.
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    Schrankentreue Berechnung der Exponentialfunktion wesentlich-nichtnegativer Matrizen (1981)
    Springer
    Computing 26 (1981), S. 57-66 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract An algorithm is proposed for computation of the exponential of a matrixX which uses the well known continued fraction expansion of tanhX. ForX essentially-nonnegative the following is proved: In interval arithmetic the algorithm is feasible, numerically convergent and bound conserving; after possibly a few initial steps it gives alternatively lower and upper bounds to the exact result.
    Notes: Zusammenfassung Es wird ein Algorithmus zur Berechnung der Exponentialfunktion von MatrizenX vorgeschlagen, der die Kettenbruch-Entwicklung von tanhX benutzt. IstX wesentlich-nichtnegativ, dann gilt: Der Algorithmus ist in Intervall-Arithmetik durchführbar, numerisch konvergent und schrankentreu; von einem Index an liefert er alternierend untere und obere Schranken für das exakte Ergebnis.
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    On the convergence of some methods for determining zeros of order-convex operators (1981)
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    Computing 26 (1981), S. 45-56 
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    ISSN: 1436-5057
    Keywords: Order-convex operator ; Banach space ; Existence ; Convergence ; Operator equation ; partially ordered topological linear space ; 65J15 ; 47H17 ; 47H07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung SeiF:X→Y ein ordnungskonvexer Operator, woX, Y halbgeordnete Banachräume sind. Es werden zwei verwandte Verfahren zur Lösung der GleichungF(x)=0 diskutiert, von denen eines schon von Pasquali beschrieben worden ist (s. [2]), das andere von Wolfe [12]. Existenz- und Konvergenzsätze für diese Verfahren sind dargestellt und mit Hilfe von Beispielen illustriert. Ferner liegen einige Bemerkungen über ein Verfahren von Traub vor, das auch schon von Wolfe diskutiert worden ist [12].
    Notes: Abstract LetF:X→Y be an order-convex operator, whereX, Y are partially ordered Banach spaces. Two related methods for the solution ofF(x)=0 are discussed, one of which has been studied by Pasquali (see [2]) and the other by Wolfe [12]. Existence-convergence theorems for the methods are given, and these are illustrated with the aid of example. Some remarks are also made on a method due to Traub [7] which has also been discussed by Wolfe [12].
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    Computer methods for efficient sampling from largely arbitrary statistical distributions (1981)
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    Computing 26 (1981), S. 19-31 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Gegeben sei ein Pseudo-Zufallszahlen-Generator, der gleichverteilte StichprobenU aus dem Intervall (0, 1) liefert, und eine statistische Verteilung, beschrieben durch ihre VerteilungsfunktionF(x). Dann erzeugt die InversionsmethodeX←F −1(U) Stichproben vonF(x). Ein Verfahren wird entwickelt, das “Guide”-Tafeln erstellt, mit dem Ziel, diese Inversion zu ermöglichen, so daß das Verfahren für beliebigeF(x) effizient wird. Für diskrete Verteilungen sind diese Tafeln klein und leicht zu erstellen, und der entstehende Stichproben-Algorithmus kann mit bekannten allgemeinen Verfahren gut konkurrieren. Stetige Verteilungen erfordern längere Vorbereitungszeiten und mehr Speicherplatz für die Tafeln. Diese werden mit Hilfe gegebener Wahrscheinlichkeitsdichtenf(x) vorbereitet. Die Methode ist anwendbar auf “vernünftige”f(x), einschließlich der normalerweise in der Statistik vorkommenden Fälle. Aufgrund der angeführten Rechenerfahrung mit Poisson-, Normal-, Gamma- und Cauchy-Verteilungen zeigt sich, daß unser allgemeines Verfahren fast so schnell ist, wie die besten bekannten Methoden, die speziell auf diese Verteilungen zugeschnitten wurden.
    Notes: Abstract Given a basic pseudo-random number generator which returns uniformly distributed samplesU from the interval (0, 1) and a statistical distribution as defined by its distribution functionF(x). Then the inversion methodX←F −1 (U) produces samples fromF(x). A procedure is developed which prepares “guide tables” in order to facilitate this inversion so that sampling becomes efficient for arbitraryF(x). For discrete distributions these tables are small and easy to set up, and the resulting sampling algorithm compares well with known general methods. Continuous distributions require longer set-up times and more space for tables. These are prepared using given probability densitiesf(x). The method can cope with “reasonable”f(x) including most cases which are commonly encountered in statistics. The reported computational experience, on Poisson, Normal, Gamma and Cauchy distributions, indicates that our general routine is almost as fast as the best known sampling algorithms which were specially designed for these distributions.
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    An algorithm for computing functions of triangular matrices (1981)
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    Computing 26 (1981), S. 67-71 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Berechnung von beliebigen Funktionen dreieckiger Matrizen ist rekursiveweise ermöglicht mittels einfacher Eigenschaften, dagelegt in diesem Bericht.
    Notes: Abstract Any function of a triangular matrix can be recursively calculated on the basis of simple properties stated in this paper.
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    On the natural interpolation formula for cauchy type singular integral equations of the first kind (1981)
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    Computing 26 (1981), S. 73-77 
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    ISSN: 1436-5057
    Keywords: Cauchy type singular integral equations ; natural interpolation formulae ; Gauss-Chebyshev quadrature rule ; Nyström (quadrature) method for integral equations ; direct numerical solution of Cauchy type singular integral equations ; Primary: 65R20 ; Secondary: 45E05, 45L10, 65D05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eine singuläre Integralgleichung erster Art vom Cauchy-Typ kann entweder direkt, mittels einer Gaußschen numerischen Integrationsformel, oder durch Reduktion auf eine äquivalente Fredholmsche Integralgleichung zweiter Art, wo die Nyström-Methode anwendbar ist, gelöst werden. In dieser Arbeit wird bewiesen, daß unter geeigneten und sinnvollen Bedingungen die Ausdrücke der unbekannten Funktion der Integralgleichung, die einerseits bei den natürlichen Integrationsformeln der direkten Methode und anderseits bei der Nyström-Methode entstehen, im ganzen Integrationsintervall gleich sind.
    Notes: Abstract A Cauchy type singular integral equation of the first kind can be numerically solved either directly, through the use of a Gaussian numerical integration rule, or by reduction to an equivalent Fredholm integral equation of the second kind, where the Nyström method is applicable. In this note it is proved that under appropriate but reasonable conditions the expressions of the unknown function of the integral equation, resulting from the natural interpolation formulae of the direct method, as well as of the Nyström method, are identical along the whole integration interval.
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    Strong solvability of interval linear programming problems (1981)
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    Computing 26 (1981), S. 79-82 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden notwendige und hinreichende Bedingungen für das Problem der linearen Optimierung mit Intervallkoeffizienten angegeben, bei denen jedes Problem der linearen Optimierung, dessen Koeffizienten in gegebenen Intervallen fixiert werden, eine optimale Lösung besitzt.
    Notes: Abstract Necessary and sufficient conditions for a linear programming problem whose parameters (both in constraints and in the objective function) are prescribed by intervals are given under which any linear programming problem with parameters being fixed in these intervals has a finite optimum.
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    A note on regular resolution (1981)
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    Computing 26 (1981), S. 87-89 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Tseitin [3] und Galil [1] haben gezeigt, daß es in der Aussagenlogik für unendlich vielen KlausenmengenS(n) der Längen gibt, so daß jeder reguläre Resolutionsbeweis fürS(n) mindestens 2 cn (für einec〉0) verschiedene Klausen enthält. Wir geben hier einen einfacheren Beweis für die viel schwächere aber dennoch nichtpolynomiale Schranke 2 clog 2 n an.
    Notes: Abstract Tseitin [3] and Galil [1] have proven that for infinitely manyn there is a set of clausesS(n) of the propositional calculus of lengthn such that any regular resolution proof ofS(n) produces at least 2 cn distinct new clauses for somec〉0. We show that it is possible to obtain a much weaker but still non-polynomial bound of 2 clog 2 n by a simpler argument.
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    Derivatives of functions by derivatives of linear positive operators (1981)
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    Computing 26 (1981), S. 83-86 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir wenden den Satz, daß für eine Segmentfunktionf, deren SegmentableitungD(f) auf dem Segment [0, 1] von oben beschränkt ist, der Hausdorff-Abstand zwischenD(f) und der Ableitung eines linearen Operators durch den Modul derH-Stetigkeit vonD(f) und Konstante nach oben beschränkt ist, an auf Bernstein-Polynome und Mirakyan-Szász-Operatoren.
    Notes: Abstract Given a segment functionf, whose segment-derivative is bounded from above on the segment [0, 1] we applicate the theorem, that the Hausdorff distance betweenD(f) and the derivative of a linear operator is bounded from above by the modulus of H-continuity ofD(f) and some constants, to Bernstein polynomials and Mirakyan-Szász-operators.
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    An adaptive, multi-level method for elliptic boundary value problems (1981)
    Springer
    Computing 26 (1981), S. 91-105 
    Details
    ISSN: 1436-5057
    Keywords: 65N20 ; Adaptive mesh refinement ; multigrid methods ; finite element methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Unterprogramm PLTMG ist ein FORTRAN-Programm zur Lösung selbstadjungierter elliptischer Randwertprobleme für beliebige Bereiche desR 2. Es basiert auf einer stückweise-linearen Finite-Element-Methode, einer adaptiven Gitterverfeinerungsmethode und einer mehrstufigen iterativen Methode zur Lösung des resultierenden Systems linearer Gleichungen. In dieser Arbeit wird die Methode beschrieben, und einige numerische Ergebnisse und Vergleiche werden dargelegt.
    Notes: Abstract Subroutine PLTMG is a Fortran program for solving self-adjoint elliptic boundary value problems in general regions ofR 2. It is based on a piecewise linear triangle finite element method, an adaptive grid refinement procedure, and a multi-level iterative method to solve the resulting sets of linear equations. In this work we describe the method and present some numerical results and comparisons.
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    URL: http://dx.doi.org/10.1007/BF02241777
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    On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems (1981)
    Springer
    Computing 26 (1981), S. 123-139 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Benutzung algebraischer Eigenwerte zur näherungsweisen Berechnung der Eigenwerte von Sturm-Liouville-Operatoren ist bekanntlich nur für die Grundschwingung und einige weitere Harmonische zufriedenstellend. In dieser Arbeit zeigen wir, wie man den asymptotischen Fehler, der bei verwandten aber einfachen Sturm-Liouville-Operatoren auftritt, dazu benutzen kann, um gewisse Klassen algebraischer Eigenwerte so zu korrigieren, daß die gleichmäßig gute Approximationen liefern.
    Notes: Abstract The use of algebraic eigenvalues to approximate the eigenvalues of Sturm-Liouville operators is known to be satisfactory only when approximations to the fundamental and the first few harmonics are required. In this paper, we show how the asymptotic error associated with related but simpler Sturm-Liouville operators can be used to correct certain classes of algebraic eigenvalues to yield uniformly valid approximations.
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    Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter (1981)
    Springer
    Computing 26 (1981), S. 107-121 
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    ISSN: 1436-5057
    Keywords: Primary: 65 H ; Secondary: 47 H ; Turning points ; Newton-like methods ; continuation methods ; local convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die RaumkurveL werde implizit durch das nichtlineare (n, n+1)-SystemH(u)=0 definiert. Es wird ein neues direktes Newton-ähnliches Verfahren zur Bestimmung der Rückkehrpunkte vonL beschrieben, das pro Schritt lediglich die Berechnung einer Jacobimatrix und 5 Funktionswerten vonH erfordert. Außerdem ist pro Schritt ein lineares Gleichungssystem der Dimensionn+1 mit 4 verschiedenen rechten Seiten zu lösen. Unter passenden voraussetzungen wird die lokale undQ-quadratische Konvergenz des Verfahrens bewiesen, sofern eine gewisse Diskretisierungsschrittweise geeignet gewählt wird. Zwei numerische Beispiele bestätigen die theoretischen Resultate.
    Notes: Abstract Let the space curveL be defined implicitly by the (n, n+1) nonlinear systemH(u)=0. A new direct Newton-like method for computing turning points ofL is described that requires per step only the evaluation of one Jacobian and 5 function values ofH. Moreover, a linear system of dimensionn+1 with 4 different right hand sides has to be solved per step. Under suitable conditions the method is shown to converge locally withQ-order two if a certain discretization stepsize is appropriately chosen. Two numerical examples confirm the theoretical results.
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    URL: http://dx.doi.org/10.1007/BF02241778
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    Two general methods for dynamizing decomposable searching problems (1981)
    Springer
    Computing 26 (1981), S. 155-166 
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    ISSN: 1436-5057
    Keywords: decomposable searching problem ; dynamization ; merging ; quad-trees ; k-d trees ; halfspaces ; maximal elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir definieren zwei Klassen zerlegbarer Suchprobleme und untersuchen, wie man diese Probleme effizient dynamisch lösen könnte. Für die erste Klasse (DD) zeigen wir, daß man sowohl das Einfügen als auch das Streichen von einzelnen Elementen im Zeitmittel effizient durchführen kann. Für die zweite Klasse (MD) zeigen wir zudem, daß man mit der Benützung einer schnellen Mischungsprozedur die Effizienz noch um ein wenig verbessern kann. Alss Anwendungen zeigen wir z. B. die effiziente Dynamisierung von Quadbäumen und vom gemeinsamen Durchschnitt endlich vieler Halbebenen in der Ebene.
    Notes: Abstract We define two classes of decomposable searching problems and consider ways of efficiently dynamizing them. For the first class, DD, we show that both insertions and deletions can be processed efficiently. For the second class, MD, we exploit a merge technique to obtain better insertion times. We also give a number of examples of problems to which the methods apply, including the dynamic maintenance of quadtrees and of the common intersection of finitely many halfspaces in the plane.
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    URL: http://dx.doi.org/10.1007/BF02241781
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    A globally and quadratically convergent algorithm for general nonlinear programming problems (1981)
    Springer
    Computing 26 (1981), S. 141-153 
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    ISSN: 1436-5057
    Keywords: 90C30 ; 65K05 ; Nonlinear programming algorithms ; penalty algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit beschreibt einen Algorithmus zur Minimierung einer nichtlinearen Funktion mit nichtlinearen Ungleichungen und Gleichungen als Nebenbedingungen. Die vorgeschlagene Methode hat die Eigenschaft, daß sie unter schwachen Voraussetzungen gegen einen Kuhn-Tucker-Punkt des betrachteten Optimierungsproblems konvergiert und unter stärkeren Voraussetzungen eine quadratische Konvergenzgeschwindigkeit aufweist. Ähnlich wie eine vor kurzem von Rosen vorgeschlagene Methode benutzt der Algorithmus eine Straffunktion, um einen Punkt in der Nähe der optimalen Lösung zu berechnen und schaltet dann auf Robinsons Methode um. Die neue Methode hat gegenüber dem Verfahren von Rosen zwei neue Eigenschaften. Erstens wird der richtige Wert des Parameters in der Straffunktion automatisch gefunden. Zweitens enthalten die mit der Methode von Robinson gelösten Teilprobleme nur lineare Gleichungen als Nebenbedingungen. Die Teilprobleme können daher besonders leicht gelöst werden. Vorläufige numerische Ergebnisse werden berichtet.
    Notes: Abstract This paper presents an algorithm for the minimization of a nonlinear objective function subject to nonlinear inequality and equality constraints. The proposed method has the two distinguishing properties that, under weak assumptions, it converges to a Kuhn-Tucker point for the problem and under somewhat stronger assumptions, the rate of convergence is quadratic. The method is similar to a recent method proposed by Rosen in that it begins by using a penalty function approach to generate a point in a neighborhood of the optimum and then switches to Robinson's method. The new method has two new features not shared by Rosen's method. First, a correct choice of penalty function parameters is constructed automatically, thus guaranteeing global convergence to a stationary point. Second, the linearly constrained subproblems solved by the Robinson method normally contain linear inequality constraints while for the method presented here, only linear equality constraints are required. That is, in a certain sense, the new method “knows” which of the linear inequality constraints will be active in the subproblems. The subproblems may thus be solved in an especially efficient manner. Preliminary computational results are presented.
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    Solving linear systems by methods based on a probabilistic interpretation (1981)
    Springer
    Computing 26 (1981), S. 209-225 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, wie das probabilistische Konzept der Stoppzeit eines Zufallsprozesses für eine iterative Methode zur Lösung eines Systems linearer Gleichungen herangezogen werden kann. Alle bekannten iterativen Näherungsmethoden zur Lösung linearer Gleichungssysteme, wie z. B. die Blockmethoden nach Jakobi und Gauss-Seidel und Überrelaxationsmethoden, entsprechen verschieden gewählten Stoppzeiten. Das probabilistische Verfahren bietet die Möglichkeit, Lösungstechniken für die spezielle Struktur des Problems zu adaptieren. Darüber hinaus führen die vorgeschlagenen Methoden zu einer schnelleren Konvergenz.
    Notes: Abstract In this paper it is demonstrated how the probabilistic concept of a stopping time in a random process may be used to generate an iterative method for solving a system of linear equations. Actually all known iterative approximation methods for solving linear equations are generated by various choices of a stopping time e. g. the point and block Jacobi methods, the point and block Gauss-Seidel Methods and overrelaxation methods are covered. The probabilistic approach offers—in a natural way—the possibility of adapting the solution technique to the special structure of the problem. Moreover, posterior bounds for the solution are constructed, which lead to faster convergence of the approximations than with usual prior bounds.
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    URL: http://dx.doi.org/10.1007/BF02243479
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    Bounding the slope of polynomial operators and some applications (1981)
    Springer
    Computing 26 (1981), S. 227-237 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden mehrere systematische Möglichkeiten angegeben, die es erlauben, bei der Verwendung der intervallmäßigen Auswertung der Ableitung in Iterationsverfahren gewisse Intervalle durch reelle Zahlen zu ersetzen. Dadurch wird im allgemeinen die Konvergenz beschleunigt. Die gleiche Problemstellung wurde bereits von einem anderen Ausgangspunkt ausgehend in [5] betrachtet.
    Notes: Abstract We discuss several systematic possibilities for removing certain intervals when using an interval expression of the derivative in iterative methods. In general, the speed of convergence is accelerated in this way. Starting from a different point of view the same problem has been treated recently in [5].
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    Optimal segmented polynomial L s -approximations (1981)
    Springer
    Computing 26 (1981), S. 239-246 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden charakteristische Eigenschaften solcher Approximationen gegeben. Ein Algorithmus, der gute, aber nicht unbedingt beste Approximationen liefert, wird diskutiert.
    Notes: Abstract Characteristic properties of such approximations are given. An algorithm providing good, but not necessarily best, approximations is also discussed.
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    Families of fifth order Nyström methods for y″=f(x, y) and intervals of periodicity (1981)
    Springer
    Computing 26 (1981), S. 247-256 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden sämtliche Nyström-Methoden fünfter Ordnung füry″=f(x, y) angegeben, welche vier Funktionsauswertungen pro Schritt benötigen. Es wird gezeigt, daß sich darunter nur eine einzige mit einem nichtleeren Periodizitätsintervall befindet.
    Notes: Abstract In this paper all fifth order Nyström methods fory″=f(x, y) based on four evaluations off are presented. Furthermore, we prove that out of these methods there is only one with a non-vanishing interval of periodicity.
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    URL: http://dx.doi.org/10.1007/BF02243482
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  • 94
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    Bemerkung zur Differentiation von intervallwertigen Funktionen (1981)
    Springer
    Computing 26 (1981), S. 271-274 
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    ISSN: 1436-5057
    Keywords: 65 G 10 ; Differentiation ; interval valued functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract This paper is concerned with relations between several versions of differentiation of interval valued functions.
    Notes: Zusammenfassung Es werden Beziehungen zwischen verschiedenen Ableitungsbegriffen für intervallwertige Funktionen angegeben.
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    URL: http://dx.doi.org/10.1007/BF02243485
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    On the accurate determination of nonisolated solutions of nonlinear equations (1981)
    Springer
    Computing 26 (1981), S. 315-326 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine einfache, aber wirkungsvolle Methode zur exakten Lösung eines nichtlinearen Gleichungssystems, dessen Funktionalmatrix in der Lösung singulär ist, vorgestellt. Dies wird durch eine Vergrößerung des Gleichungssystems zu einem höherdimensionalen Gleichungssystem, dessen entsprechende Lösung isoliert ist, erreicht. Diese Lösung kann daher z. B. mit dem Newton-Verfahren, das lokal mindestens quadratisch konvergent und selbstkorrigierend ist, mit großer Genauigkeit bestimmt werden.
    Notes: Abstract A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.
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    FORTRAN for contemporary numerical computation (1981)
    Springer
    Computing 26 (1981), S. 277-314 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In numerischen Rechnungen treten neben den ganzen Zahlen häufig auch reelle und komplexe Zahlen, reelle und komplexe Intervalle sowie Vektoren und Matrizen über diesen Mengen auf. In der vorliegenden Arbeit erweitern wir die ProgrammierspracheFORTRAN so, daß Ausdrücke mit Operanden und Operatoren für all diese Typen (Datenmengen) akzeptiert werden. Wir beginnen mit einer kurzen Zusammenstellung dieser Räume und der arithmetischen Verknüpfungen in den Teilmengen, welche auf einem Rechner darstellbar sind. Es folgt dann eine allgemeine Beschreibung der Spracherweiterung sowie der neuen Standardfunktionen und Standardformelfunktionen für die zusätzlichen Datentypen. Im zweiten Teil der Arbeit geben wir dann die vollständige Syntax für die erweiterte Sprache in Form von leicht lesbaren Syntaxdiagrammen an. Wir erläutern auch die Semantik der Spracherweiterung.
    Notes: Abstract In addition to the integers, the real and complex numbers, the real segments (intervals) and complex segments as well as vectors and matrices over all of these comprise the fundamental data types in computation. We extendFORTRAN so that it accepts operands and operators for all of these types as primitives in expressions. We briefly review the spaces corresponding to these data types and the definitions of the arithmetic operations in their computer representable subsets. Then we give a general description of the language extension including the additional basic external functions and intrinsic functions for the new data types. Following this we give the syntax for the extended language in the form of easily traceable syntax diagrams. Comments on the semantics are also included.
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    Asymptotisch optimale Relaxationsparameter bei nichtlinearen SOR-Verfahren (Newton-SOR-Verfahren) (1981)
    Springer
    Computing 26 (1981), S. 327-332 
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    ISSN: 1436-5057
    Keywords: 65 N 20 (Numerical solution of nonlinear boundary value problems)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract For nonlinear SOR-methods (Newton-SOR-methods) we discuss the problem how to get asymptotic optimal relaxation parameters ω(v). Here the matrix of the linear system at each step of iteration has not to be consistently ordered, we only assume symmetry and definitness. Our parameters are easy to compute and fixed for all steps. As an example nonlinear elliptic differential equations and their numerical solution by the finite element method or classical difference approximation are considered.
    Notes: Zusammenfassung Für nichtlineare SOR-Verfahren (Newton-SOR-Verfahren) wird ein einfaches Verfahren zur Berechnung asymptotisch optimaler Relaxationsparameter ω(v) erörtert. Hierbei muß die Matrix des in jedem Iterationsschritt auftretenden linearen Gleichungssystems nicht notwendig konsistent geordnet sein, wir setzen nur Symmetrie und Definitheit voraus. Es zeigt sich, daß die Parameter unabhängig von der jeweiligen Iterationsstufe ν gewählt werden können. Ihre Berechnung wird im Zusammenhang mit der numerischen Lösung nichtlinearer elliptischer Differentialgleichungen vermittels der Methode der finiten Elemente oder der klassischen Differentenapproximation diskutiert.
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    On the R-order of coupled sequences (1981)
    Springer
    Computing 26 (1981), S. 333-342 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für Folgen aus einem iterativen Näherungsverfahren, die einem mit Hilfe von Potenzfunktionen beschreibbaren System von Ungleichungen genügen, wird gezeigt, daß ihre R-Ordnung mindestens gleich dem Spektralradius der Matrix aus den Exponenten ist, sofern ein zum Spektralradius gehörender Eigenvektor mit ausschließlich positiven Komponenten existiert.
    Notes: Abstract The R-order of sequences, coupled by a system (1) of difference inequalities, is shown to be at least equal to the spectral radius of the matrix of the exponents if a positive eigenvector belonging to the spectral radius exists.
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    A reliable rosenbrock integrator for stiff differential equations (1981)
    Springer
    Computing 26 (1981), S. 355-360 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, daß die Sicherheit eines Programmes für gewöhnliche Differentialgleichungen durch einen einfachen Trick wesentlich erhöht werden kann. Mit Hilfe dieser Idee und einer A-stabilen Rosenbrock-Formel haben wir ein kleines Programm geschrieben, welches gute numerische Resultate liefert.
    Notes: Abstract This note points out that the reliability of step-by-step integrators for ordinary differential equations can be increased considerably by a simple trick. We incorporated this idea into a program based on an A-stable Rosenbrock formula. This program comprises about 100 statements only and gives good numerical results.
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    A note on linear expected time algorithms for finding convex hulls (1981)
    Springer
    Computing 26 (1981), S. 361-366 
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    ISSN: 1436-5057
    Keywords: Convex hull ; average complexity ; geometrical complexity ; algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir betrachtenn als unabhängig identisch verteilte Zufallsvektoren imR d mit der gemeinsamen Verteilungsdichtef. Die mittlere Konvexität eines Algorithmus zur Bestimmung der konvexen Hülle dieser Punkte seiE (C). Die meisten bekannten Algorithmen genügen für gewisse Klassen von Dichten der BedingungE (C)=0(n). In dieser Mitteilung zeigen wirE (C)=0(n) für Algorithmen, die im Vorlauf einen „Wegwerf-Schritt” benützen, wennf auf jedem nicht ausgearteten Rechteck desR 2 beschränkt ist und positiven Abstand von 0 besitzt.
    Notes: Abstract Considern independent identically distributed random vectors fromR d with common densityf, and letE (C) be the average complexity of an algorithm that finds the convex hull of these points. Most well-known algorithms satisfyE (C)=0(n) for certain classes of densities. In this note, we show thatE (C)=0(n) for algorithms that use a “throw-away” pre-processing step whenf is bounded away from 0 and ∞ on any nondegenerate rectangle ofR 2.
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    URL: http://dx.doi.org/10.1007/BF02237955
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