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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 141-149 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It was hypothesized in an earlier work that sensory perception can occur only when the perceiving system is uncertain about the nature of the event being perceived. In the absence of any uncertainty, perception will not take place. The response of the sensory afferent neuron (impulse transmission rate) was calculated using Shannon's measure of uncertainty or entropy. It will now be shown that when the event being perceived is the position and momentum of a particle, Shannon's measure of uncertainty leads to the Heisenberg Uncertainty relationship.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 239-244 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is not unusual for several classifications to be given for the same collection of objects. We present a method, called majority rule, which can be used to define a consensus of these classifications. We also discuss some mathematical properties of this consensus tree.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 259-270 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The dependence of the spatial concentration profiles of morphogens on a characteristic dimension is obtained by continuation techniques for Gierer and Meinhardt's activator-inhibitor model of morphogenesis. The study of the behaviour of the system during growth, where the linear and exponential increase of the characteristic dimension is considered, revealed that more complex patterns of morphogen spatial concentrations appear regularly in a reproducible way.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 271-278 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Computer models have been used by various authors to simulate both the growth of normal cellular tissue and the development of cancerous cells within normal tissue. As these models were the result of considerable idealization, the purpose of the present paper is to propose a model in which the degree of simplification is relaxed: the features of simultaneous growth, and cell growth whose rate depends on the free absorbing periphery of the cell are introduced. Simulation experiments have been conducted using the model, and the results are presented.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 341-346 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 279-325 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 375-388 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The irreversible Michaelis-Menten reaction is studied by the use of the method of multiple scales. Three stages of the reaction are identified, one of which is studied in detail. The results are compared with those of two earlier analyses.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 11
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 389-400 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A numerical study of the coupled nerve fibre problem is given which verifies and extends the perturbation theory of Luzader. Pulses on adjacent fibres can couple together with two possible stable pulse separations.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 12
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 401-413 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A possible mechanism for effects of microwave radiation on the auditory system is the generation of field-induced forces at interfaces that divide materials of dissimilar electrical properties. A general expression for these “Maxwell stresses” is derived and then used to calculate the approximate magnitude of field-induced force within the organ of Corti during microwave exposure. Comparison of the results with data on the force needed to excite cochlear hair cells indicates auditory responses could be evoked by this mechanism at power densities near the threshold of rf hearing sensations.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 13
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 415-426 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A definition of homogeneity for neural networks is given which permits their construction as group quotients. The significance of this for neural dynamics is discussed.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 14
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 447-461 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The left ventricle is represented as a cylinder contracting both radially and longitudinally. A simple method is indicated to derive an expression for the rate of change of the kinetic energy of this three-dimensional model, which quantity can be used as an index for the study of the contractile behaviour of the myocardium. An application to the study of muscle mechanics is also indicated.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 15
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 463-485 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 16
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 513-516 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 17
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 59-67 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of computational complexity and certain explicitly-stated hypotheses imply limitations on the information processing power of biological systems. Parallelism, special purpose organization, and analog mechanisms may provide speedup critical for life processes, but have little power in the face of exponential growth. We show that “polynomially simulatable” biological systems cannot exhibit dynamic behavior which produces the solution of an intractable problem. The argument implies that parallelism does not allow biological systems to defeat the exponential explosion, but rather is important because it allows polynomial time algorithms to be used more efficiently.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 18
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 81-88 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A correlation matrix analysis is applied to the base sequence of MS2 and ϕX174 in comparison with sets of simulated sequences with different degrees of constaint Significant differences between a codified sequence, and a statistical one in terms of the “correlation matrix” for sets of different length cannot be found. This result is analysed in terms of nucleotide sequences with different levels of informational content.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 19
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 101-109 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 20
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 111-116 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 21
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 89-99 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The mean first passage time for free diffusion can be derived directly by solving a simple analogue steady state problem. In this problem the diffusion starting region is considered as a time independent source of diffusing particles and the diffusion target assumes the behaviour of a perfectly absorbing sink. It is shown here that the transit time between the source and the sink, which in this particular problem is equal to the ratio between the holdup of the system and the total flux, is identical to the Brownian movement concept of the mean first passage time for free diffusion. This established identity considerably facilitates the derivation and investigation of the timing of diffusion in complicated structures such as those commonly found in living organisms.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 22
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 121-123 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 23
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 117-120 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 24
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 201-211 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 25
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 213-232 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Two simple models are proposed and analysed, in which it is shown that the formation of a new polymer, resulting from an “error” in the template action mechanism of production of an old polymer, may compromise the stability of the initial system under specific conditions, in the context of prebiotic evolution. Autocatalysis is shown to be a “selective advantage”, enabling the “mutant” to dominate in concentration and even replace the initial polymer. The addition of a third molecule playing the role of a catalyst causes hysteresis effects.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 26
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 165-181 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The problem of extinction of the prey population in a microbial predator-prey interaction in a chemostat has been examined. Usual deterministic lumped parameter models were used for the dynamics of the chemostat for large numbers of the two populations; the generalized birth and death stochastic process was employed for the description of the random variations at small prey numbers. Extinction probabilities of the prey population were calculated for different holding times and chemostat volumes, and their dependence upon the growth parameters of the two populations was studied. It was found that extinction was possible when the Monod model was used for the specific growth rate of the predators as a function of the prey number density. On the other hand, the decrease of the feeding activity of the predators at low prey densities predicted by the multiple saturation model acts as a regulatory factor that prevents extinction of the prey. In view of the fact that extinction of the prey has never been observed in the laboratory, the latter model seems more appropriate to describe the dynamics of microbial predation.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 27
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 233-238 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract During exposures of the eye to light, the choroidal circulation may have a regulatory influence on the retinal temperature. This is investigated using a mathematical model and a finite-difference technique. It is predicted that the choroidal blood flow a small effect on retinal temperature, which may be important.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 28
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 427-446 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 29
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 503-512 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract We consider a one-compartment system with stochastic transfer rate characterized either by Gaussian or by two-level jump process and study the time evolution of the (statistical) moments of the (random) amount of the substance present in the system. The effect of the coloured as well as of the white noise is investigated and it is found that the presence of stochasticity in the transfer rate parameter increases the relaxation time of the system. Finally, we obtain the conditions for the stability of the system in the moment sense.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 30
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 487-501 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model is described in which damage to a single intracellular locus can lead to a tumorigenic transformation. Assuming a large number of independent intracellular loci to be at risk and assuming that damage to a locus sufficient to cause a tumorigenic transformation occurs with probability greater than zero for all doses greater than zero, leads to the use of the Weibull distribution to characterize the probability of a nonspontaneous tumorigenic cellular transformation occurring after exposure to a given dose of carcinogen. The excess lifetime tumor incidence (i.e., the proportion of tumor bearers) above the spontaneous incidence is used as an estimate of the non-spontaneous incidence and is characterized by a tumor incidence function that represents the probability of occurrence of one or more non-spontaneous tumorigenic cellular transformations amongN(D) independent surviving cells per individual, after exposure to a doseD of carcinogen. The tumor incidence function is fitted to published data for the excess tumor incidence after exposure of animals or humans to ionizing radiation and after exposure of animals to chemical carcinogens.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 31
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 549-561 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.
    Materialart: Digitale Medien
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  • 32
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 563-577 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with the pulsatile blood flow in the lung alveolar sheets by idealizing each of them as a channel covered by porous media. As the blood flow in the lung is of low Reynolds number, a creeping flow is assumed in the channel. The analytical and numerical results for the velocity and pressure distribution in the porous medium are presented. The effect of an imposed slip condition is also studied. Comparisons with the corresponding results for the steady-state case are made at the end.
    Materialart: Digitale Medien
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  • 33
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 579-591 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
    Materialart: Digitale Medien
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  • 34
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 705-715 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The preceding paper (Thorn, 1981) has shown that in a linear pharmacokinetic system with a multimodal impulse response the peak drug level may sometimes be smaller with slower rates of injection. This paper presents two theorems on this paradoxical injection rate effect where the injection is a constant infusion of finite duration. The first theorem establishes a graphical method for determining whether a given impulse response will give a paradoxical injection rate effect; and the second establishes that the maximum paradoxical increase in peak drug level is by a factor of two. It is further shown that in order to approach this maximum paradoxical increase the impulse response must contain two isolated, sharp, narrow pulses of approximately equal area. Some examples of bimodal arterial dye-dilution curves from the literature are discussed as impulse responses; and there is also a discussion of the behavior of drug level maxima and minima at different injection rates.
    Materialart: Digitale Medien
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  • 35
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 693-703 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate.
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  • 36
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    Bulletin of mathematical biology 43 (1981), S. 33-45 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 37
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 21-32 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 38
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 69-79 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 39
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 151-163 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 40
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 183-199 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 41
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 245-247 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 42
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 249-257 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 43
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 327-340 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 44
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 347-360 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 45
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 371-372 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 46
    Digitale Medien
    Digitale Medien
    Springer
    Bulletin of mathematical biology 43 (1981), S. 361-370 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 47
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 372-373 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 48
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 517-548 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 49
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 593-610 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 50
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 611-618 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 51
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    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 619-639 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 52
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    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 641-650 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 53
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 681-691 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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).
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 54
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    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 665-680 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 55
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    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 651-664 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 56
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    Bulletin of mathematical biology 43 (1981), S. 717-717 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 57
    Digitale Medien
    Digitale Medien
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    Bulletin of mathematical biology 43 (1981), S. 719-719 
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 58
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    Digitale Medien
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    Mathematical programming 21 (1981), S. 190-203 
    ISSN: 1436-4646
    Schlagwort(e): Complementarity Problem ; Cones ; Topological Degree
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 59
    Digitale Medien
    Digitale Medien
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    Mathematical programming 21 (1981), S. 233-234 
    ISSN: 1436-4646
    Schlagwort(e): Polytope ; Subdivision ; Simplex ; Volume ; Centroid
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 60
    Digitale Medien
    Digitale Medien
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    Mathematical programming 21 (1981), S. 301-318 
    ISSN: 1436-4646
    Schlagwort(e): Semi-infinite Programs ; Open Helly-type Theorems ; Finite Subprograms ; Convex Programs ; Multi-criteria Programs ; Quasi-convex Programs ; Quasi-differentiable Programs
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
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  • 61
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    Digitale Medien
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    Mathematical programming 21 (1981), S. 348-356 
    ISSN: 1436-4646
    Schlagwort(e): Multi-extremal Optimization ; Multinomial Distribution ; Bayes Estimate ; Monte Carlo
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 62
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    Digitale Medien
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    Mathematical programming 21 (1981), S. 120-120 
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 63
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    Digitale Medien
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    Mathematical programming 21 (1981), S. 319-330 
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Geometric Programming ; Duality Theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 64
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    Mathematical programming 21 (1981), S. 1-18 
    ISSN: 1436-4646
    Schlagwort(e): Game Theory ; Cost Allocation ; Spanning Tree
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 65
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    Mathematical programming 21 (1981), S. 119-119 
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 66
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    Digitale Medien
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    Mathematical programming 21 (1981), S. 121-136 
    ISSN: 1436-4646
    Schlagwort(e): Linear Programming ; Polynomial Algorithms ; Total Unimodularity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 67
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    Mathematical programming 21 (1981), S. 182-189 
    ISSN: 1436-4646
    Schlagwort(e): Equilibrium ; Linear Monetary Economy ; Linear Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 68
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    Mathematical programming 21 (1981), S. 229-232 
    ISSN: 1436-4646
    Schlagwort(e): Primal Feasible Basis ; Dual Feasible Basis ; Basic Variable ; Nonbasic Variable ; Optimal Basic Solution
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 69
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    Mathematical programming 21 (1981), S. 240-240 
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 70
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    Mathematical programming 21 (1981), S. 241-261 
    ISSN: 1436-4646
    Schlagwort(e): Dual problem ; Duality Theory ; Optimality Conditions ; Price Functions ; Nonlinear Programming ; Integer Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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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  • 71
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    Mathematical programming 21 (1981), S. 358-358 
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
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    Monatshefte für Mathematik 92 (1981), S. 323-328 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The quaternion algebraB[j] over a commutative ringB with 1 defined byS. Parimala andR. Sridharan is generalized in two directions: (1) the ringB may be non-commutative with 1, and (2)j 2 may be any invertible element (not necessarily −1). LetG={ϱ} be an automorphism group ofB of order 2, andA={b inB|ϱ (b)=b}. LetB[j] be a generalized quaternion algebra such thataj ϱ (a) for eacha inB. It will be shown thatB is Galois (for non-commutative ring extensions) overA which is contained in the center ofB if and only ifB[j] is Azumaya overA. Also,A[j] is a splitting ring forB[j] such thatA[j] is Galois overA. Moreover, we shall determine which automorphism group ofA[j] is a Galois group.
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  • 73
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    OR spectrum 2 (1981), S. 235-249 
    ISSN: 1436-6304
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Heute verfügbare Softwarepakete der gemischt-ganzzahligen Programmierung sind noch nicht fortgeschritten genug, um als Black Boxes behandelt zu werden. Ihre Effizienz kann durch eine gründliche Kenntnis ihrer Funktionsweise und der dem Benutzer angebotenen Freiheitsgrade beträchtlich gesteigert werden. Diese Veröffentlichung beschreibt zuerst die Auswahlmöglichkeiten der zugrundeliegenden Branch und Bound Methode in sieben repräsentativen MIP-Systemen und demonstriert anhand illustrativer Beispiele deren Anwendung, deren Nutzen und deren Fußangeln. Im Anschluß werden Proceduren und administrative Funktionen in kommerziellen MIP-Modulen, soweit sie dem Benutzereinfluß unterliegen, dargestellt. Ein Ausblick auf zukünftige Entwicklungen zeigt, wie sich Akzeptanz und Leistungvon MIP-Software steigern können. Schließlich werden einige Kriterien zur Aufwandsabschätzung vor und in verschiedenen Stadien während des Lösungsprozesses vorgeschlagen.
    Notizen: Summary Today's mixed integer programming software packages are still not sophisticated enough to be treated as black boxes. Their efficiency can be augmented considerably by a deep knowledge of their functioning and the degrees of freedom they offer to the user. This paper describes at first the choices of the underlying branch and bound method in seven representative MIP-systems and demonstrates their usage, their profitability and their catches at illustrative examples. An account follows of the procedures and administrative facilities of commercial MIP-modules as far as they are submitted to user influence. An outlook is given on future developments, which can further improve the acceptance and the performance of MIP-software. Finally, some effort assessment criteria are proposed, which help judging the amount of work ahead before and at different stages during the solution process.
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    OR spectrum 3 (1981), S. 153-160 
    ISSN: 1436-6304
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Ziel der Personalplanung ist ein besserer Ausgleich zwischen Personalbedarf und -Verfügbarkeit. Zulässige Vorhersagen für den zukünftigen Bedarf zu erhalten, ist der schwierige Anteil der Personalplanung. Daher ist es also wichtig, den Informationsbedarf über die Zukunft zu kennen, um in der Gegenwart gute Entscheidungen zu treffen. Wie genau sollte nun unsere Kenntnis des zukünftigen Personalbedarfs sein und wie weit in die Zukunft sollte sie reichen? Die letzte Frage hängt direkt mit dem Planungshorizont zusammen. In dieser Arbeit wird diese für ein hierarchisches Personalplanungssystem mit zwei Laufbahnstufen untersucht: Neueinstellung und eine Beförderungspolitik, die von der Anzahl der Jahre der Betriebszugehörigkeit abhängt. Ziel der Einstellungspolitik ist es, den Stellenplan für beide Stufen möglichst gut zu erfüllen. Abweichungen vom Stellenplan werden mit dazu proportionalen Strafkosten belegt. Die alleinige Steuerungsmöglichkeit für das Personalplanungssystem besteht in der Änderung der Einstellungspolitik. Für den Fall, daß alle Beschäftigten dieselben Karrierevoraussetzungen besitzen, können sehr allgemeine Ergebnisse erhalten werden, da das Problem dem mit nur einer Laufbahnstufe nahezu äquivalent ist. Für den allgemeineren Fall kann man Ergebnisse für den Planungshorizont nur dann erreichen, wenn zusätzliche Bedingungen an die Strafkosten und Ziele gestellt werden. Der allgemeinste Zweistufenfall ist formal äquivalent zu einem Produktionsglättungsproblem ohne Lagerhaltung und mit einer unteren Schranke für die Differenz zwischen den Kosten zweier aufeinanderfolgenden Perioden.
    Notizen: Summary The purpose of manpower planning is to get a better matching between manpowerrequirement and manpower availability. The difficult part of manpower planning is to get reliable forecasts for future manpower requirement. It is important, therefore, to know what information one needs about the future to make good decisions now. How detailed should our knowledge of future manpower requirement be and of how far in the future? The last point is directly related to the problem of the planning horizon. This problem is investigated in this paper for a hierarchical manpower system with two grades, recruitment at the bottom and a promotion policy formulated in the grade-age (number of years in grade one). There is a goal on the total content of the system and a goal on the content of the second level. These goals may be interpreted as the future requirements. The penalties for deviations from the goals are assumed to be proportional to these deviations. The only way to control the system is by recruitment. For the case where all employees have the same career pattern one can get rather general results since this problem is almost equivalent to the case with only one grade. For the more general case it is only possible to get planning horizon results if conditions are added on the penalty functions and the goal patterns. The general two-level case appears to be equivalent to the production-smoothing problem without inventory with a lower bound on the difference between the hiring in two subsequent periods.
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    Monatshefte für Mathematik 91 (1981), S. 1-9 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In [8] the author extended the concept of “neighbouring functions” (cp. [9]) to the case of several variables. Using these results it is shown that under some weak conditions a multiplicative functionf in two variables has a mean-value different from zero if and only if the two multiplicative functionsf 1(n)=f(n, 1) andf 2(n)=f(1,n) have mean-values different from zero. Applications to theorems ofDelange [3],Elliott [6] andDaboussi [1] are given.
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    Monatshefte für Mathematik 91 (1981), S. 11-18 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract No general statement can be made about the speed with which convergence takes place in the Ergodic Theorem, in the sense that one can never be sure that convergence of the remainder to zero is fast enough to make, through term-by-term multiplication, any divergent series become convergent. As a corollary we obtain the nonexistence in general of the one-sided ergodic Hilbert transform; that is, there is no pointwise “nonhomogeneous ergodic theorem”.
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    Monatshefte für Mathematik 91 (1981), S. 19-37 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We determine the class of all locally compact stable planesM of positive dimensiond≤4 which admit a reflection at each point of some open setU $$U \subseteq M$$ M. Apart from the expected possibilities (planes defined by real and complex hermitian forms, and almost projective translation planes), one obtains (subplanes of)H. Salzmann's modified real hyperbolic planes [14; 5.3] and one exceptional plane which was not known before. The caseU=M has been treated [9] and is reproved here in a simpler way. The solution to the problem indicated in the title constitutes the main step in the proof of our results.
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    Monatshefte für Mathematik 91 (1981), S. 39-71 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Already in 1933J. Blank found all ruled surfaces with two conjugated families of plane shade lines. In the late sixtiesH. Brauner solved a similar problem by determining all algebraic surfaces with only one family of plane shade lines. — We consider here only differentiable ruled surfaces withBrauner's condition, that carry at least one continuous family of plane shade lines. By using methods of projective differential geometry, algebra and synthetic projective geometry, it is possible to find all projective representatives of those surfaces. Although the assumption ofBrauner is much weaker thanBlank's, each of these surfaces is an analytic, ruled surface ofBlank.
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    Monatshefte für Mathematik 91 (1981), S. 73-76 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract IfV is a variety of Ω-groups and ifG∈V then one can study the algebraG V [x] of polynomials overG andx inV. With respect to addition and substitution,G V [x] is a near-ring. Its zero-symmetric part can excellently be used to describe generated ideals. Also, we study maximal left ideals and get a general result on the structure ofG V [V].
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    Monatshefte für Mathematik 91 (1981), S. 77-78 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract As a simple corollary to the main result of [4] we describe the structure of commutative semigroups which are isomorphic to their nontrivial homomorphic images.
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  • 81
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    Monatshefte für Mathematik 91 (1981), S. 105-117 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Someq-analogues of the classical Laguerre-polynomials are studied from the point of view of umbral calculus.
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    Monatshefte für Mathematik 91 (1981), S. 89-103 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In part I algebraic structures (esp. rings) on the sets of polynomials and formal power series on an at most countable alphabetA are considered. Given a partial order onA the words ofA * are mixed together in consistence with it. It is shown that the structures derived are associative iff the given partial order is of linear type. The coefficients appearing at these operations are identified as generalizations of the ordinary binomial coefficients and a number of relations involving them are listed up. (Part II will bring a generalization ofRota's theory of polynomial sequences of binomial type to the structures studied in I. In Part III the theory of special binomial systems will be continued until the analogue of Lagrange inversion and a short development of generalized Sheffer polynomials will be given).
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    Monatshefte für Mathematik 91 (1981), S. 119-129 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract LetG be a compact group with dual object Γ. A decomposition of Γ into pairwise disjoint finite sets provides a way of defining partial sums of Fourier series onG. We employ a theorem of Olevskii to present a condition on such a decomposition which, if satisfied, guarantees that the corresponding Lebesgue constants are unbounded. We apply this to certain summation methods on tori and compact connected semisimple Lie groups.
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    Monatshefte für Mathematik 91 (1981), S. 131-138 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The paper is a study of the limiting behaviour of the [n t]-th iterates of the well-known Post-Widder operatorsL n, x used in the real inversion of the Laplace transform. It is shown that the limiting operators constitute a semigroup ∼T t;t≥0∼ of class (C 0) on a family ∼C α,β; α, β〉0∼ of Banach spaces. Applications of the semigroup structure lead to a pointwise saturation theorem forL n, x and a characterization of convex functions inC α, β through an inequality involving the action ofL n, x.
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    Monatshefte für Mathematik 91 (1981), S. 139-152 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The tool of van der Corput's difference theorem in the theory of uniform distribution is his so-called fundamental inequality.Kemperman showed that even the non-constructive proofs of the difference theorem byBass, Bertrandias andCigler implicitly use a more general form of van der Corput's fundamental inequality. In this article, the inequality which constitutes the basis of the difference theorem will be proved under a very general setting, applications will be demonstrated in connection with the uniform distribution of products of linear forms and a quantitative version of the difference theorem, i. e. an estimation of discrepancies, will be derived.
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    Monatshefte für Mathematik 91 (1981), S. 153-166 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This note contains certain conditions for unit-regularity and for selfinjective regular rings to have bounded index (such rings have many interesting properties [9]). Sufficient conditions are also given for rings to be Noetherian, Artinian and quasi-Frobeniusian.
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    Monatshefte für Mathematik 91 (1981), S. 167-170 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
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    Monatshefte für Mathematik 91 (1981), S. 171-179 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper we will investigate (k+1)-dimensional generalized ruled surfaces generated by a one-parameter family ofk-dimensional linear subspaces of then-dimensional Euclidean spaceE n . Some results which are well-known for developable surfaces are proved for generalized ruled surfaces: Generalized developable surfaces are locally either cyclinders, cones or tangent surfaces. Each regular surface on a generalized ruled surface Φ is locally Euclidean if and only if Φ is developable. Each locally Euclidean hypersurface is a generalized developable hypersurface. Furthermore, the hypersurfaces with vanishing Gaussian curvature and the locally Euclidean hypersurfaces on generalized rule hypersurfaces will be characterized.
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    Monatshefte für Mathematik 91 (1981), S. 197-202 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract LetR be an order of an algebraic number field of degreen over ℚ,V ann-dimensional real vector space and ℊ the class of lattices inV which are free rank 1 modules overR. For certain ordersR and distance functionsd onV a method of computingd-minimal vectors of Γ ∈ ℊ is described; further it is shown how to constructs anR-basis for Γ ∈ ℊ by comparing thed-length of vectors of Γ. An application to the computation of fundamental units and class numbers of real abelian number fields is mentioned.
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    Monatshefte für Mathematik 91 (1981), S. 181-196 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this part starting from a generalization of the binomial theorem a development of Rota's theory of polynomial sequences of binomial type to the case of countably many noncommuting variables is given. Translation invariance of operators gives the relation to the formal power series considered inI. For a special class of binomial systems there are given a number of characterizations, such as a generalized Rodrigues formula. In the case of an analogue of the Newton polynomials those are used for a study of generalized Stirling numbers. (In III the theory of binomial systems of diagonal type will be continued until an analogue of Lagrange inversion and a short development of the theory of generalized Sheffer polynomials will be given.)
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    Monatshefte für Mathematik 91 (1981), S. 203-214 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A conjecture ofH. Kleiman says that over certain fields a Galois equation of degree ≥3 is uniquely determined by its root polynomials. We prove this conjecture for prime degrees ≥3 and a somewhat smaller class of fields than Kleiman's. In this situation, the ideal of all relations between zeros of the equation has a basis containing root polynomials only, not the equation itself. Giving a large class of counterexamples of degree 4, we disprove Kleiman's conjecture in general.
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    Monatshefte für Mathematik 91 (1981), S. 215-232 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We define rectangle exchange transformations analogously to interval exchange transformations. An interval exchange transformation is a mapping of the unit interval onto itself obtained by cutting the interval up into a finite number of subintervals and rearranging the pieces. A rectangle exchange transformation is a mapping of the unit square onto itself obtained by cutting the square up into a finite number of rectangular pieces and rearranging the pieces. We give a minimality condition for rectangle exchange transformations. We deal with various examples of ergodic rectangle exchange transformations. Related questions are discussed.
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    Monatshefte für Mathematik 91 (1981), S. 233-240 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We derive a condition for a closed invariant subset of a compact dynamical system to be an attractor (resp. repellor) combining the usual Ljapunov function methods with time averages. Applications are given to concrete systems endowed with some cyclic symmetry. In particular, cooperation of the inhomogeneous hypercycle is shown.
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    Monatshefte für Mathematik 91 (1981), S. 241-251 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract LetK II denote the inner curvature of the second fundamental form of a surface in euclidean threespace and letH be the usual mean curvature. It is well known that the sphere is the only closed ovaloid satisfyingK II=H. In the present paper it is shown that the surfaces of revolution satisfyingK II=H are locally characterized by constancy of the ratio of the principal curvatures. Using previous results ofH. Hopf this implies that there exist closed analytic surfaces (which are different from the sphere) satisfying the equalityK II=H everywhere except at two flat points whereK II is not defined but limK II=0.
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    Monatshefte für Mathematik 91 (1981), S. 253-256 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
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    Monatshefte für Mathematik 91 (1981), S. 257-274 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract LetN be a real submanifold in a complex manifoldM. If the maximal complex subspaces of the tangent spaces ofM contained in the tangent spaces ofN are of constant dimension and they define a differentiable distribution, thenN is called a generic submanifold. The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds andCR-submanifolds. In this paper we initiate a study of generic submanifolds in a Kähler manifold from differential geometric point of view. Some fundamental results in this respect will be obtained.
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    Monatshefte für Mathematik 91 (1981), S. 275-289 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Given semi-normsf andg on ℝ n and a real number μ〉0. Then the successive minima off under the constraintg≤μ are defined by λ j : = inf {λ: there existj linear independent vectors inZ n withf≤λ andg≤μ}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ℝ n (without constraints) coincide with the λ j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.
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    Monatshefte für Mathematik 91 (1981), S. 291-298 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The unboundedness of the set of Lebesgue constants (norms) arising from the application of a summation method to an appropriate series implies the existence of a continuous function whose associated series fails to be summable by that method. Here it is established that the Lebesgue constantsL (t, B) arising from thet-th Borel exponential mean of Laplace series equal 23/4 π -3/2 Г(1/4)t 1/4 +O(1), ast → ∞, showing that this phenomenon (known as the Du Bois-Reymond singularity) occurs for Borel summation of Laplace series.
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    Monatshefte für Mathematik 91 (1981), S. 299-311 
    ISSN: 1436-5081
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper we consider complexes of lines in an isotropic space of degree two, i. e. a three dimensional real affine space with the metricds 2=dx 2. Using the method of differential forms we study the local differential geometry of first order and the theory of complex curves. Finally we give some applications in the theory of linear complexes.
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