ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Books
  • Articles  (21,752)
  • Other Sources
  • Springer  (21,752)
  • Frontiers
  • MDPI Publishing
  • 1975-1979  (21,752)
  • Mathematics  (21,752)
Collection
  • Books
  • Articles  (21,752)
  • Other Sources
Source
Keywords
Publisher
Years
Year
Journal
Topic
  • 1
    Electronic Resource
    Electronic Resource
    Modeling of biological tree structures (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 893-898 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462385
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Diversity and diffusion in multidimensional niche space (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 129-138 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460873
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Stochastic compartmental modeling and parameter estimation with application to cancer treatment follow-up studies (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 203-215 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we use marginal probabilities to derive expressions for the means, variances and covariances ofm-compartment systems. We also present an efficient algorithm for the estimation of the parameters of the system using time series data when measurements are available fromk of them compartments. An application of the analysis and parameter estimation procedure for a model representing the results of a cancer treatment follow-up study is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460879
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Self-organization in biological systems with multiple cellular contacts (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 193-201 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460878
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Performance criteria for optimization of cardiac assistance (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 217-227 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A performance criterion and weighting factors for the optimal cardiac assistance are investigated by applying Tellegen's network theorem and tolerance analysis on animal experimental data for left ventricular (LV) bypass on the failing heart. Two major factors with respect to cardiac assistance (total power delivered to the peripheral circulatory system, and changes in temporal pattern of ventricular contraction) are represented by two performance criteria,J 1 andJ 2 whereJ 1 relates to the sum of LV and pump power, andJ 2 relates to the “peakedness” factor of LV power. The total performance index (J) is determined as the weighted sum ofJ 1 andJ 2;J=w 1J1+w2J2. The weighting factors,w 1 andw 2, are computed as inverses of the tolerance in the performance contours with respect to improvement of stroke work per minute from pre- to post-bypass condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460880
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Catastrophe theory: Selected papers 1972–1977 (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 253-255 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460882
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Volterra-Verhulst prey-predator systems with time dependent coefficients: Diffusion type approximation and periodic solutions (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 229-251 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In treating the Volterra-Verhulst prey-predator system with time dependent coefficients, we ask how far this deterministic system represents or approximates the dynamics of the population evolving in a realistic environment which is stochastic in nature. We consider a stochastic system withsmall Gaussian noise type fluctuations. It is shown that the higher moments of the deviation of the deterministic system from the stochastic approach zero as the strength δ of the perturbation decays to zero. For any δ〉0 and allT〉0, ε〉0, the sample population paths that stay within ε distance from the deterministic path during [0,T] form a collection of positive probability. In comparing the stationary distributions of the two systems, we show that the weak limits of those of the stochastic system form a subset of those of the deterministic system. This is in analogy with a result of May connected with the stability of the two systems. Plant and rodent populations possess periodic parameters andexhibit periodic behaivor. We establish theoretically this periodicity under periodicity conditions on the coefficients and perturbing random forces. We also establish a central limit property for the prey-predator system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460881
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    A theoretical study of neural adaptation and transient responses due to inhibitory feedback (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 257-282 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Adaptation of repetitively firing sensory neurons and nerve models is correlated with specific inhibitory feedback phenomena—an electrogenic sodium pump, and post synaptic self inhibition. The quality of the adaptive responses depends on the excitation properties of the neuron in the interspike interval, or the description of these properties by the underlying impulse encoder model. THis model dependence is demonstrated by comparisons of the behavior of two classes of models; the “leaky integrator models” which assume a passive neural membrane, and the “variable-γ models”, for which the neural state of excitation varies according to first order differential equations. The complexity inherent in the variable-γ models is effectively boiled down to mathematically simple relationships which are derived from studies of the neural- and model frequency responses to small amplitude sinusoidal stimuli. It is argued, and supported with examples, that these relationships hold for impulse frequency transients resulting from more general stimulus conditions. Expressions are then derived which permit feedback parameters to be determined from impulse frequency data. In this connection, recent studies of neural dynamics are brought to bear to resolve ambiguities in data interpretation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460812
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On the measurement of shape (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 283-304 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A setQ(n) of noncongruent connected shapes, constructed from a fixed numbern of congruent regular hexagons laid edge to edge, is defined. Various measures of shape are applied toQ(n) and the results are numerically analyzed in the special casesn≦9. The concept of spatial entropy is introduced which affords a measure of the “complexity” of shape. Possible biological applications include the analysis of ecological cover,stigmergy or the complex nest-building activities of social insects and morphogenesis. Essentially any comparative study of shape, regardless of the specific application, might be carried out along the lines suggested in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460813
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Mathematical approaches to optimization of cancer chemotherapy (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 305-324 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper uses optimal control theory in conjunction with a Gompertzian type model for cellular growth to determine the optimal method of administering cycle non-specific chemotherapy or more generally the optimal durations of treatment and rest periods during chemotherapy. The performance critera employed to determine the relative merits of the therapy include not only the destruction of malignant cells, but also the sparing of a critical normal tissue. Since these criteria are at odds with one another, the solutions are found which satisfy the Pareto optimality conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460814
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Asymptotic solutions of differential equations with time delay in population dynamics (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 325-342 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Oscillations governed by generalized Volterra-Gause-Witt equations to include retardation effects in population dynamics are considered. Models containing either small or significant time delay are discussed. The Krylov-Bogoliubov-Mitropolskii perturbation method and its extension for differential equations with retarded argument is used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460815
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Time development of probability distributions for interacting species (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 357-364 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A general solution to the dynamical equation for the probability distribution associated withn interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values oft to Dirac δ-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For ann-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460817
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Nernst-planck analog equations and stationary state membrane electric potentials (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 365-385 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A set of coupled nonlinear differential equations, determining the concentration profiles and electric potentials valid for isothermal transport of ions and molecules across a diffusion barrier are formulated, using a correction to the limiting expression for chemical potential gradients and the molecular expression for frictional force. These differential equations are similar to Nernst-Planck equations and reduce to these under appropriate approximations. Solutions of these equations valid under specified conditions are presented. Expressions for permeability, concentration profiles of many ion systems are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460818
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    Global flow equations for membrane transport from local equations of motion—II. The case of a single nonelectrolyte solute plus water (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 629-640 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The global flow equations of nonequilibrium thermodynamics for a single nonelectrolyte solute and water passing through a membrane are obtained by solving the local equations of motion. The method follows that developed for the general,n-solute case in the previous paper (Mikulecky, 1978). It is easily seen in this simple case that the passage from local interactions, formulated as position dependent frictional interactions in the equations of motion, to ghe global result involves a loss of any simple way of identifying particulars about local information. Two particular cases are analyzed in further detail: the case of no interaction within the pore and the case of constant interaction for both solute and solvent across the pore. In the former case, Onsager reciprocity survives in the global result if a self-consistent definition of the partial viscosity coefficients is used, while in the latter case, reciprocity is lost. Since, in many biologically interesting cases, the presence of interaction of the type considered here is likely to occur, the reciprocity condition should not automatically be assumed to hold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462419
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells—I. Reduced systems (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 665-686 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462421
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Some results about nonlinear chemical systems represented by trees and cycles (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 641-664 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Using linear stability analysis, the qualitative stability properties of open nonlinear chemical systems, in which reactions of any order may occur, will be studied. Systems will be classified in three fundamental classes: trees, cycles and loops, according to their knot graphs. The study of the Jacobian matrix for the kinetic equations of the system shows that the symmetrizability by a particular procedure (calledD-symmetrizability) is a sufficient condition for stability. It has been proved that tree-graphs always satisfy the above condition. For the cycle-graphs, theD-symmetrizability condition leads to a cyclic relation between forward and reverse steady state flows. The stability may be assured, even if the cyclic relation is not satisfied, providing that the “symmetry breaking” be lower than an upper bound; further alternative criteria for stability of cycles have been derived. All these results are independent of the number of diffusive exchanges with the environment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462420
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    Analysis of the behaviour of Kauffman binary networks—I. State space description and the distribution of limit cycle lengths (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 687-705 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The basis of an analytical description of the behaviour of large random nets of binary elements of the type first investigated in detail by S. A. Kauffman is presented. It is shown that information about the network dynamics can be deduced from quite general considerations of the properties of the state transition graph and matrix. An expression for the matrix elements of the state transition matrix in terms of the Boolean function specification of the net is derived. Using these ideas the distribution of limit cycle lengthsl for a completely random net is calculated and shown to bex 1/l, a result which agrees well with experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462422
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Analysis of the behaviour of Kauffman binary networks—II. The state cycle fraction for networks of different connectivities (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 707-724 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The state-transition matrix description of Kauffman binary networks described in the previous paper is further developed to obtain an analytical expression for the fraction of states involved in limit cycles as a function of the network size and connectivity. The result obtained for totally connected networks agrees with that derived from quite different considerations by other workers. For low connectivity networks the results are in qualitative agreement with the experimental data of Kauffman but there is a quantitative discrepancy which remains to be resolved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462423
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    Persistence in food webs—I Lotka-Volterra food chains (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 877-891 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462384
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    Minimal oxygen consumption and optimal contractility of the heart: Theoretical approach to principle of physiological control of contractility (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 139-150 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Oxygen consumption of the left ventricle (MVO 2) was evaluated theoretically under the condition that the ventricle pumps a constant stroke volume against a constant arterial pressure, hence producing a constant external mechanical stroke work, with a widely varied contractility.MVO 2 was calculated by an empirical equation which had been inferred previously. Theoretical results indicated that the ventricle has a contractility at whichMVO 2 is minimal in spite of constant external work and therefore the mechanical efficiency as a pump is maximal. Such a contractility can be considered to be optimal from a standpoint of metabolic economy. The optimal contractility fell within the physiological range of contractility which had been observed experimentally. The result suggests a possibility that the contractility of a normal heart might be physiologically adapted to such an optimal level.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460874
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    Nonlinear diffusion in biological systems (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 151-162 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Diffusion problem with variabale diffusion coefficient in a spherical biological system is investigated. Also included in this study is the biological reaction of the Michaelis-Menten type. The problem formulated consists of a highly nonlinear differential equation which, however, can be efficiently solved by the orthogonal collocation method on a digital computer. The effects of the dimensionless governing parameters on the transient and steady state concentration responses are parametrically examined for the diffusion system with and without biological reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460875
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    Electric potential in three-dimensional electrically syncytial tissues (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 163-181 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of calculating the potential induced in an electrical syncytium by a point source of current is studied. The interiors of the many interconnected cells are treated as one continuum with resistivity ρ i . The interdigitated extracellular space is treated as a second continuum of resistivity ρ e , occupying the same overall volume, coupled to the first via the resistanceR m and capacitanceC m of the cell membranes. The intra- and extracellular potentials are then solutions to a pair of coupled partial differential equations. The equations are uncoupled, yielding a cable equation for the transmembrane potential and a Poisson equation for a second auxiliary potential. For an unbounded syncytium the potential for a step function source is obtained in terms of error functions. For a spherical syncytium of radiusa, bounded by a membrane with surface resistanceR a, and capacitanceC a, expansions are obtained in spherical harmonics and spherical Bessel functions. For ɛ=ρ ia/R a and β=ρ i /ρ e small, an asymptotic expansion of the potential is developed. The results are compared to earlier results for a spherical cell as well as to microelectrode measurements of the lens of the eye.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460876
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    Electric potential in cylindrical syncytia and muscle fibers (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 183-192 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The model developed in an earlier paper using two coupled partial differential equations for calculating the intracellular and extracellular electric potentials in a syncytium is applied here to cylindrical geometry. Eigenfunction expansions are obtained for the potentials resulting from an intracellular point source of current. The required orthogonality relations for the two sets of coupled radial eigenfunctions are derived. The model is applied to the structure composed of the interior and the transverse tubules of a muscle fiber. Asymtotic expansions for ζ and β→0 are obtained, where ζ is the product of the effective intracellular resistivity, the fiber radius and the outer surface membrane admittance per unit area, and β is the ratio of the effective intracellular resistivity to that of the tubular lumen. Earlier results from the distributed circuit model of a muscle fiber are recovered when ζ and β are small, and for a nerve axon when β=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460877
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    Analysis of potassium conductance in squid giant axons (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 343-356 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Assuming a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975) and extended by McIlroy and Hahn (1978), it is shown that if the selectivity coefficient, πK, of the potassium conducting system ≃59 the permeabilityP Ks, of the periaxonal barrier of the squid giant axon for K+ ions≃(1.2±0.44)×10−4 cm sec−1 and the thickness of the periaxonal space ≃477±168 Å. Using a value (10−4 cm sec−1) ofP Ks in the foregoing range the experimental curves for the steady state membrane ionic conductance versus measured membrane potential difference (p.d.), ϕ, of Gilbert and Ehrenstein (1969) are corrected for the effect of accumulation of K+ in the periaxonal space. This correction is most marked for the axon immersed in a natural ionic environment, whose conductance curve is shifted ≃70mV along the voltage axis in the hyperpolarization direction. By assuming that the physico-chemical connection between a depolarization of the axonal membrane and the consequent membrane conductance changes is a Wien dissociative effect of the membrane's electric field on a weak electrolyte situated in the axolemma, the position of the peaks of the corrected conductance versus ϕ curves can be identified with zero membrane electric field and hence with zero p.d.across the axolemma. A set of values for the double-layer p.d.s at the axonal membrane interfaces with the external electrolytes in the vicinity of the K+ conducting pores can therefore be deduced for the various external electrolytes employed by Gilbert and Ehrenstein. A model of these double-layer p.d.s in which the membrane interfaces are assumed to possess fixed monovalent negatively charged sites, at least in the neighbourhood of the K+ conducting pores, is constructed. It is shown that, using the previously deduced values for the doublelayer p.d.s, such a model has a consistent, physically realistic solution for the distance between the fixed charged sites and for the dissociation constants of these sites in their interaction with the ions of the extramembrane electrolytes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460816
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    Mutation-absorption model of the enzyme (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 387-405 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Gradual changes in function of proteins in response to single changes in primary structure are often observed to occur and are a necessary condition for evolution by variation and natural selection at the protein level. A probabilistic (entropy theory_ analysis of the effect of changes in primary structure on three-dimensional shape and function shows that such gradualism is based on the presence of a control system in the molecule involving a definite general form of structure-function degeneracy. The assumptions of the analysis are that primary structure determines tertiary structure (or a thermal distribution of tertiary configurations and allosteric forms), tertiary structure determines function (characterized by rate and other parameters), and that certain features of tertiary structure may be specialized for particular functions. The main conclusion is that embodied in the molecule is a subsystem which serves as a buffer, absorbing mutation or other forms of genetic variation and expressing these as graceful variations in features of the shape critical for function. This buffer system may be realized by numerical redundancy of amino acids or other mechanisms which increase the redundancy of weak interactions responsible for folding, utilization of amino acids having a greater number of analogs with redundant features, or local and global structural formats which allow for more effective utilization of redundancy. The mutation-absorption model has implications for the interpretation of structure-function relations in biology, the topology of the adaptive landscape, the interpretation of isoenzymes and allozymes, the relationship between selection and neutralism in evolution, and the relation between the complexity of and energy required by biological systems and the effectiveness of evolutionary optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460819
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    Some comments on activation and inhibition (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 427-445 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of rate equations gives rise to a corresponding pattern of activation and inhibition between the state variables. We consider the converse question: to what extent does the specification of a pattern of activation and inhibition between interacting quantities determine the rate equations? Among other things, it is shown that in order to determine a closed set of rate equations, a set of integrability conditions among the interactions must be satisfied; hence there is a sense in which an activation-inhibition pattern is more general than systems of rate equations. Questions of the structural interactions, are briefly discussed. A comparison is made between the properties of such activation-inhibition patterns and those of neural networks, or more general modular automata.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460821
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    Global flow equations for membrane transport from local equations of motion: 1. The general case for (n−1) nonelectrolyte solutes plus water (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 447-447 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460822
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    A teleological explanation of Weber's law and the motor unit size law (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 407-425 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that the Weber-Fechner law. which relates the response of a sensory biosystem to the intensity of the input stimulus, can be derived from a teleological principle of minimum transentropy (maximal noise reduction) provided the relative mean fluctuation (coefficient of variation) of the input intensity can be assumed to be (approximately) constant for all feasible mean input intensities. A law is then deduced from experimental results which quantifies the relationship existing between the relative amount of activated muscle mass and the “size” (which term is clearly defined) of a newly recruited motor unit. This law is found to be formally equivalent to the Weber-Fechner law when applied to motor unit recruitment. It is then shown that, in general, the ratio of the force increment upon recruitment, to the present force output does not obey Weber's law. Finally, it is proved that the “motor unit size law” as derived in this paper implies a fixed sequential order in the recruitment of motor units and that it may be viewed as the realization, by the mammalian neuromuscular system, of a general principle of maximum grading sensitivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460820
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    Stability and selection in self-reproducing macromolecular systems (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 449-460 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458323
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    Chemical patterns in circular morphogenetic fields (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 461-468 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of the basic requirements of this model is the existence of a circular morphogenetic gradient exhibiting no discontinuity. We explain how bifur-cation theory may account for the generation of such a spatial pattern through reaction-diffusion processes. For this, we study the emergence of multiple-order bifurcations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458324
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    Bistability in fluctuating environments. Implications in tumor immunology (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 469-490 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We analyze under different environmental conditions the occurrence of bistability, i.e. of two simultaneously stables steady states, in a biological model system which describes the immunological interactions of neoplastic-target cells and cytotoxic-effector cells. As a result of environmental fluctuations such complex biological systems may undergo drastic modifications of their steady state properties. In particular, when the variance of fluctuations increases around a well defined mean value, transition phenomena appear which are absent in the usual bifurcation diagrams. The properties of the non-fluctuating systems can no longer be considered as a first approximation of the properties of the real system. Interestingly, in the case of the model, these transitions correspond to a rejection of tumor cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458325
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    Some results on light penetration of an absorbing medium (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 517-523 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two results on light penetration of an absorbing medium are presented in this paper: (1) It is shown, using the general light penetration law of Mannet al. (1977), that a random distribution of absorbing bodies (cells, leaves, etc.) is most efficient at intercepting direct beam (parallel) light. (2) A transmission coefficient is added to the general law in a manner similar to Monteith's (1965). This leads to the partitioning of the radiation regime beneath an absorbing medium into unintercepted, once intercepted, twice intercepted, etc., components. We are thus enabled to calculate the mean radiation intensity beneath the absorbing medium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458327
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    Compartmental models with multiple sources of stochastic variability: The one-compartment, time invariant hazard rate case (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 491-515 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Previous stochastic compartmental models have introduced the primary source of stochasticity through either a probabilistic transfer mechanism or a random rate coefficient. This paper combines these primary sources into a unified stochastic compartmental model. Twelve different stochastic models are produced by combining various sources of stochasticity and the mean value and the covariance for each of the twelve models is derived. The covariance of each model has a different form whereby the individual sources of stochasticity are identificable from data. The various stochastic models are illustrated for certain specified distributions of the rate coefficient and of the initial count. Several properties of the models are derived and discussed. Among these is the fact that the expected count of a model with a random rate coefficient will always exceed the expected count of a model with a fixed coefficient evaluated at the mean rate. A general modeling strategy for the onecompartment, time invariant hazard rate is also proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458326
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    Coexistence of photosynthetic microorganisms with growth rates depending on the spectral quality of light (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 525-542 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new equation for the growth rate of photosynthetic microorganisms is derived. It is based on a series formulation of the mechanism of photosynthesis and it has the form of a functional of the spectral qualities of light. Using this functional to model their growth it is shown that populations of photosynthetic microorganisms can coexist in the same homogeneous environment even though they compete for the available light.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458328
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    Stochastic prey-predator relationships: A random evolution approach (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 543-554 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The formalism and results of the theory of random evolutions are used to establish and investigate a model for two randomly interacting populations. The asymptotic stability of the expected solution is studied and contrasted to that of the associated deterministic system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458329
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    On a mathematical model describing the aggregation of amoebae (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 555-571 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper an extension of a mathematical model of Keller and Segel (1970) describing the aggregation of amoebae is presented. In their paper (Keller and Segel, 1970) they showed that the onset of the aggregation could be viewed as a spatial instability. Their instability condition involved diffusion constants of the cyclic AMP and of the amoebae as well as a constant describing the chemotactic behavior of the amoebae. In our case we consider a temporal instability that depends only on the kinetics of cyclic AMP production, degradation and transport through the cell wall. Our model then explains the oscillatory behavior of the cyclic AMP in well-stirred suspensions of amoebae. In addition we discuss existence and non-existence of nonuniform steady states of the nonlinear parabolic system involved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458330
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Markov branching processes with varying growth rates (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 607-610 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A branching processZ(t) which behaves as Markov branching processesZ 1(t) andZ 2(t) during the free and dead times of a counter process is considered. Expression forE[Z(t)] is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458333
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    The method of harmonic balance applied to coupled asymmetrical van der Pol oscillators for intestinal modelling (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 573-589 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The spontaneous electrical rhythms recorded from the gastro-intestinal tract of humans and animals have been successfully modelled by an array of interconnected van der Pol oscillators. To account for asymmetry in the recorded waveforms (with particular reference to the human small intestine) an additional term in the van der Pol dynamics has been included. It is shown that the method of harmonic balance can be used to give analytical results for this asymmetrical condition. The non-linear algebraic equations are solved by hill-climbing to give values of d.c., fundamental and second harmonic amplitudes together with the entrained frequency. The results correlate well with actual measurements made on an analogue simulation by three different methods for waveshape factors of 0.1 and 1.0
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458331
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    A mathematical study of non-equimolar ternary gas diffusion (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 591-606 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In view of the increasing evidence that multicomponent diffusion effects could be significant in biological gas exchange systems, a non-equimolar film model of multicomponent diffusion was derived. “Osmotic” ternary diffusion was studied for the gas systems He−N2−O2, He−SF6−O2, and N2−SF6−O2. Diffusional fluxes and concentration profiles were calculated under both the “square-root” and the “product” flux conditions. Results were also compared with those obtained using the equimolar flux condition. It was found that the greater the difference of the diffusibilities between the two active components in a system, the greater the osmotic fluxes, and also the more alinear the concentration profiles. These results support the suggestion that the “product” condition applies to molecular diffusion in free space, the “square-root” condition to molecular diffusion in pores, and the equimolar flux condition to closed diffusion systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458332
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    On stochastic compartmental modeling (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 611-613 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This communication contains a proof of the fact that the coefficient of variation of the contents of a compartment of a stochastic compartmental model with deterministic rate parameters is small for large populations. We can therefore conclude that the use of stochastic compartmental models is not of great consequence in the case of systems involving large populations when only the randomness of the transfer mechanism is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458334
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    Catastrophe theory and its applications (Surveys and reference works in mathematics2) (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 615-616 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458335
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    Existence of a limiting pattern for a system of nonlinear equations describing interpopulation competition (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 617-628 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of arbitrarily many nonlinear ordinary differential equations which can be interpreted as describing competition between populations is studied here. It is found that limits exist for the system given specified constraints on the “signal function” which describes input-output relations at the level of single populations. Existence of limits is shown by means of a function which records which variable in the system is growing fastest at a given time i.e. who is winning the competition. Generalizations are discussed to sigmoid signal functions which appear in models of pattern discrimination by neuron populations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462418
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    On the distribution of the general irreversiblen-compartmental model having time-dependent transition probabilities (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 737-749 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The cumulant generating function and first two moments are derived for the stochastic distribution of units in a general irreversiblen-compartment model with time-dependent transition probabilities. In this model, a unit in the first compartment can transfer to any one of the remainingn−1 compartments and a unit in the second compartment can transfer to any of the remainingn−2 compartments and so on. In addition, a unit can enter or leave the system through any compartment. The work is related to previous research and a numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462425
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    On the study of two interacting populations one of which acts independently of the other (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 725-735 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Many ecological and biological systems can be studied in terms of a bivariate stochastic branching process, {X 1 (t), X 2 (t)}, each of whose components (or populations) varies in magnitude according to the laws of a generalized birth-death process. Of particular interest is such a model in which the birth and death rates of the first population,X 1, are constant while those of the second population,X 2, exhibit a functional dependence upon the magnitude of the first. It is shown, first, that the existence of the stochastic mean of a birth death process implies the existence of all higher moments. The values of all the factorial moments of such a process are then determined. The moments of the dependent population of the bivariate process are given in terms of its expectation and the joint probability density function of the process is determined. It is possible, therefore, to use Bayesian techniques to infer conclusions about the independent population, given information about the variation of the dependent one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462424
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    On feasible random ecosystems (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 751-755 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Only a fraction of the total number of equilibrium solutions of the differential system which describes the populations of species in an ecosystem are feasible: that is only a fraction of the solutions give non-negative values for all the populations. The feasible equilibrium solutions of a generalized logistic equation are considered for the limiting cases of strongly and weakly interacting species. It is found that only about one third of all the possible species are generally expected to be present (i.e. to have non-zero populations) at any given equilibrium solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462426
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    Book reviews (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 757-759 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462427
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    Selection in systems of self-reproducing macromolecules under the constraint of controlled energy fluxes (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 761-766 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider a method for selection among a collection of self-reproducing macromolecular information carriers. The information carriers are assumed subject to the general constraint in which the fluxes of the energy rich monomers used in the syntheses of the information carriers are controlled externally. The constraint forces a competition among the various macromolecular species and a Darwinian like selection takes place. We show that the overall selective behaviour is independent of the specific form of the constraint. A general criteria for selection is given and we show that the selection process may generally be characterized by an optimization principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462374
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    The bifurcation diagram of a model chemical reaction—II. Two dimensional time-periodic patterns (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 767-790 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The bifurcation equations of a general reaction-diffusion system are derived for a circular surface. Particular attention is directed to the deformation of the circular boundary into an elliptic shape. This leads to a new bifurcation diagram which may involve secondary bifurcation, but which retains however the basic characteristics of the solutions for the circular case. Numerical simulations of the various coexisting, time-periodic and space-dependent solutions, are presented for a simple model reaction and circular geometry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462375
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    Some remarks on the dynamics of molecular self-organization (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 803-812 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dynamics of a self-organizing molecular system is described in terms of its normal modes. Each normal mode is associated with a certain eigenvalue, the average of which reflects most directly the overall process of self-organization. For the temporal change of this quantity a maximum principle holds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462377
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    A simple anatomical model of muscle, and the effects of internal pressure (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 791-802 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The purpose of this study is to investigate the relationship between the structure of muscle and its function, especially with regard to the influence of the internal pressure when a muscle contracts. A model is constructed based on the anatomy of muscle. For difference shapes of muscle, but of equal volume, the muscle features (i.e. force exerted etc.) are computed after every contraction step. A function for the internal pressure is also calculated. The internal pressure influences the structure of the muscle which also depends in a certain way upon the function of the muscle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462376
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    Periodic auto-immune hemolytic anemia: An induced dynamical disease (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 829-834 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Experimentally induced auto-immune hemolytic anemia (AIHA) in rabbits is characterized either by constant depressed erythrocyte numbers, or by oscillatory erythrocyte numbers about a depressed level (periodic auto-immune hemolytic anemia). Here the experimetallys observed characteristics of AIHA are satisfactorily accounted for by a simple model for erythropoiesis, assuming only the peripheral erythrocyte destruction rate is elevated with all other parameters normal. The onset of periodic AIHA is identified with the occurrence of a Hopf bifurcation in the model dynamics for certain values of the erythrocyte destruction rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462379
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    On the gating currents and the dipole transitions (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 841-848 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Gating current is considered to be due to the transition of dipoles, which are coupled with the membrane matrix. Based on previous theory of nerve excitation, the equation for gating current is derived; the charge displacement equation and the time constant of the gating current are also derived. Agreement with experimental data is good.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462381
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    Explicit solutions of Fisher's equation for a special wave speed (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 835-840 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The travelling waves for Fisher's equation are shown to be of a simple nature for the special wave speeds $$c = \pm 5/\sqrt {(6)} $$ . In this case the equation is shown to be of Painlevé type, i.e. solutions admit only poles as movable singularities. The general solution for this wave speed is found and a method is presented that can be applied to the solution of other nonlinear equations of biological and physical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462380
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    An exact analysis of the sliding motion in contractile system: A simplified model of muscle system (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 813-828 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system involving two kinds of sliding filaments is analysed with special attention to the actomyosin system. Rigorous results are obtained about the statistical effect originating from many active sites distributed on both filaments. It is necessary for the occurrence of smooth motion in sliding filament that the spatial periods of active sites on both filaments are relatively incommensurable, and that the number of active sites on each filament is large enough. Sufficient conditions for smooth contraction are derived under the assumption that both filaments are rigid; this is called rigid rod approximation in the present paper. The elastic mode of the filaments, during the sliding process, is analysed by perturbation theory based on the rigid rod approximation. A stochastic theory is briefly discussed in reference to the cooperative generation of contractile force, which is concerned in Hill's relation of muscle contraction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462378
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    Some models for selection of biological macromolecules with time varying constraints (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 849-859 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider some models for selection in self-reproducing macromolecular systems subject to time varying environmental constraints. We show that many of the results concerning selection obtained previously for stationary constraints may be generalized and that the over-all selective behaviour even in complex enzyme coupled systems is basically the same under the time varying external conditions as it is in the stationary case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462382
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    Some stability conditions for discrete-time single species models (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 861-875 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Standard results relating to the stability of autonomous first order difference equations are restated here with slight modifications so as to apply directly to equations in which the state variable remains positive. Some simple and effective tests for both local and global stability of these first order difference equations are presented. The main results are illustrated with examples drawn from population biology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462383
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    A teleological explanation of Weber's law and the motor unit size law (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. i 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462387
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    Analytical considerations on a new class of functions for the mathematical description of the human Erythrocyte's profile during the osmotic, “disk-sphere” transition (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 899-904 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analytical procedure is used to derive a class of functions for the shapes of the cross section of the human red cell during its osmotic swelling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462386
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 59
    Electronic Resource
    Electronic Resource
    Tenth International Symposium on Mathematical Programming (1979)
    Springer
    Mathematical programming 16 (1979), S. 261-261 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582113
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 60
    Electronic Resource
    Electronic Resource
    On a class of least-element complementarity problems (1979)
    Springer
    Mathematical programming 16 (1979), S. 111-126 
    Details
    ISSN: 1436-4646
    Keywords: Least Element ; Linear Complementarity ; Quadratic Programs ; Special Structure ; Applications ; Computational Experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The present paper studies the linear complementarity problem of finding vectorsx andy inR + n such thatc + Dx + y ≧ 0,b − x ≧ 0 andx T (c + Dx + y) = y T (b − x) = 0 whereD is aZ-matrix andb 〉 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented. Finally, applications and computational experience with its implementation are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582097
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 61
    Electronic Resource
    Electronic Resource
    Editorial policy (1979)
    Springer
    Mathematical programming 16 (1979), S. 139-139 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582103
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 62
    Electronic Resource
    Electronic Resource
    An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy (1979)
    Springer
    Mathematical programming 16 (1979), S. 190-209 
    Details
    ISSN: 1436-4646
    Keywords: Algorithm ; Piecewise Linear ; Complementary Pivot ; Equilibrium Model ; Trade ; Production Prices ; Linear Programming ; Fixed Point Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The general equilibrium model is approximated as a piecewise linear convex model and solved from the point of view of welfare economics using linear programming and fixed point methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582108
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 63
    Electronic Resource
    Electronic Resource
    Referees 1978 (1979)
    Springer
    Mathematical programming 16 (1979), S. 260-260 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582112
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 64
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 16 (1979), S. 263-263 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582115
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 65
    Electronic Resource
    Electronic Resource
    On the solution of some (parametric) linear complementarity problems with applications to portfolio selection, structural engineering and actuarial graduation (1979)
    Springer
    Mathematical programming 16 (1979), S. 325-347 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Computational Results ; Structural Engineering ; Applications ; Portfolio Selection ; Actuarial Graduation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we discuss three applications of a class of (parametric) linear complementarity problems arising independently from such diverse areas as portfolio selection, structural engineering and actuarial graduation. After explaining how the complementarity problems emerge in these applications, we perform some analytical comparisons (based on operation counts and storage requirements) of several existing algorithms for solving this class of complementarity problems. We shall also present computational results to support the analytical comparisons. Finally, we deduce some conclusions about the general performance of these algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582119
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 66
    Electronic Resource
    Electronic Resource
    Call for papers: Conference on Combinatorial Optimization (1979)
    Springer
    Mathematical programming 16 (1979), S. 136-136 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582101
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 67
    Electronic Resource
    Electronic Resource
    A stable method for solving certain constrained least squares problems (1979)
    Springer
    Mathematical programming 16 (1979), S. 141-158 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Least Squares Problems ; Positive Semidefinite Quadratic Programming ; Orthogonal Factorization ; Reorthogonalization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a feasible descent algorithm for solving certain constrained least squares problems. These problems are specially structured quadratic programming problems with positive semidefinite Hessian matrices that are allowed to be singular. The algorithm generates a finite sequence of subproblems that are solved using the numerically stable technique of orthogonal factorization with reorthogonalization and Given's transformation updating.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582105
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 68
    Electronic Resource
    Electronic Resource
    The number of solutions of a class of linear complementarity problems (1979)
    Springer
    Mathematical programming 17 (1979), S. 104-105 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Number of Solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588229
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 69
    Electronic Resource
    Electronic Resource
    Some remarks on condensation methods for geometric programs (1979)
    Springer
    Mathematical programming 17 (1979), S. 109-113 
    Details
    ISSN: 1436-4646
    Keywords: Geometric Programs ; Kuhn—Tucker Conditions ; Condensation Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to present some points of clarification of a recently presented algorithm for geometric programs [7]. While presenting the clarification, we are able to identify the behavior of condensation type algorithms for generalized geometric programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588231
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 70
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 17 (1979), S. 121-121 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588236
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 71
    Electronic Resource
    Electronic Resource
    A multiplier method with automatic limitation of penalty growth (1979)
    Springer
    Mathematical programming 17 (1979), S. 140-155 
    Details
    ISSN: 1436-4646
    Keywords: Multiplier Methods ; Adaptive Penalization ; Nonlinear Programming ; Quadratic Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a multiplier method for solving optimization problems with equality and inequality constraints. The method realizes all the good features that were foreseen by R. Fletcher for this type of algorithm in the past, but which suffers from none of the drawbacks of the earlier attempts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588240
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 72
    Electronic Resource
    Electronic Resource
    Editorial policy (1979)
    Springer
    Mathematical programming 17 (1979), S. 401-401 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588261
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 73
    Electronic Resource
    Electronic Resource
    Goal programming sensitivity analysis using interval penalty weights (1979)
    Springer
    Mathematical programming 17 (1979), S. 16-31 
    Details
    ISSN: 1436-4646
    Keywords: Goal Programming ; Sensitivity Analysis ; Vector-Maximum Algorithms ; Multiple Objective Linear Programming ; Multiple Criteria Decision Making
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents an application of the vector-maximum research [4–8] to the sensitivity analysis of goal programming problems as several of the criterion function penalty weights are simultaneously and independently varied. A generalized goal programming capability is presented and a six-stage analytic procedure is described. The problem is generalized in the sense that the regular goal programming penalty weights can be expanded to intervals if desired. The solution procedure is new in that it depends upon an algorithm for the vector-maximum problem, “criterion cone” contraction procedures, and “filtering” techniques. Together they are able to generate and process all extreme points on the portion of the surface of the goal programming “augmented” feasible region corresponding to the interval penalty weights specified. In effect, the procedure and adapted algorithm of this paper delivers to goal programming an operational power of sensitivity analysis not previously available to users. A numerical example is provided in order to illustrate the computerized application of the total goal programming procedure outlined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588223
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 74
    Electronic Resource
    Electronic Resource
    On the symmetric travelling salesman problem II: Lifting theorems and facets (1979)
    Springer
    Mathematical programming 16 (1979), S. 281-302 
    Details
    ISSN: 1436-4646
    Keywords: Linear Inequalities ; Convex Polytopes ; Facets ; Lifting Theorems ; Travelling Salesman Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Four lifting theorems are derived for the symmetric travelling salesman polytope. They provide constructions and state conditions under which a linear inequality which defines a facet of then-city travelling salesman polytope retains its facetial property for the (n + m)-city travelling salesman polytope, wherem ≥ 1 is an arbitrary integer. In particular, they permit a proof that all subtour-elimination as well as comb inequalities define facets of the convex hull of tours of then-city travelling salesman problem, wheren is an arbitrary integer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582117
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 75
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 16 (1979), S. 388-388 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582127
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 76
    Electronic Resource
    Electronic Resource
    A construction method in parametric programming (1979)
    Springer
    Mathematical programming 16 (1979), S. 21-36 
    Details
    ISSN: 1436-4646
    Keywords: Parametric Linear Programming ; Construction Method ; Degeneracy ; Primal Lexicographic Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider a linear programming problem, with two parameters in the objective function, and present an algorithm for finding the decomposition of the parameter space into maximal polyhedral areas in which particular basic solutions are optimal. Special attention is paid to fill up areas of degenerate solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582092
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 77
    Electronic Resource
    Electronic Resource
    A computational study of active set strategies in nonlinear programming with linear constraints (1979)
    Springer
    Mathematical programming 16 (1979), S. 81-97 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Linear Constraints ; Computational Experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An essential part of many iterative methods for linearly constrained nonlinear programming problems is a procedure for determining those inequality constraints which will be “active” (that is, satisfied as equalities) at each iteration. We discuss experiments in which we used several strategies for identifying active constraints in conjunction with two well-known algorithms for linearly constrained optimization. The results indicate that in most cases a strategy which keeps the number of constraints in the active set as small as possible is computationally most efficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582095
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 78
    Electronic Resource
    Electronic Resource
    A direct dual method for the mixed plant location problem with some side constraints (1979)
    Springer
    Mathematical programming 17 (1979), S. 198-228 
    Details
    ISSN: 1436-4646
    Keywords: Plant Location ; Dual Method ; Orthogonality Conditions ; Enumeration ; Computational Results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The mixed plant location problem (mixed in the sense of allowing capacitated as well as uncapacitated plants) is a difficult and important mixed integer problem. We give a direct dual method, consisting of several phases (each of which appears essential for some data), to resolve a strong relaxed form of the problem with additional constraints over the integer variables (user specified, or derived from the data themselves). When all features of the algorithm are employed, there appears to be no difficulty with problems of 100 plants, even in an inefficient computer implementation. The primal solutions which we derive from the orthogonality conditions and a simple greedy heuristic are almost always much better than those we obtain from a standard relaxed problem in the Lagrangean sense. With an enumeration code in an efficient implementation we would expect to be capable of resolving very large problems (of perhaps up to 500 or 1000 plants) to within practically well acceptable tolerances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588244
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 79
    Electronic Resource
    Electronic Resource
    Mathematical programming study 10 (1979)
    Springer
    Mathematical programming 17 (1979), S. 115-118 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588233
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 80
    Electronic Resource
    Electronic Resource
    Optimization: Techniques and Applications (1979)
    Springer
    Mathematical programming 17 (1979), S. 122-122 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588237
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 81
    Electronic Resource
    Electronic Resource
    On perfect graphs and polyhedra with (0, 1)-valued extreme points (1979)
    Springer
    Mathematical programming 17 (1979), S. 239-242 
    Details
    ISSN: 1436-4646
    Keywords: Anti-Blocking ; Perfect Graphs ; Polyhedra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetC andA be (0, 1)-valued matrices with no zero columns. Fulkerson has shown that the extreme points of {x: Cx ≤ 1,x ≥ 0} are given by the rows ofA and their projections and the extreme points of {x: Ax ≤ 1,x ≥ 0} are given by the rows ofC and their projections if and only if the maximal rows ofC andA are the incidence vectors of maximal cliques and anticliques, respectively, of a perfect graph. This theorem is discussed and a new proof is given for the “only if” implication.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588246
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 82
    Electronic Resource
    Electronic Resource
    Exact penalty functions in nonlinear programming (1979)
    Springer
    Mathematical programming 17 (1979), S. 251-269 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Penalty Functions ; Exact Penalty Functions ; Constraint Qualification ; Second Order Optimality Conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that the existence of a strict local minimum satisfying the constraint qualification of [16] or McCormick's [12] second order sufficient optimality condition implies the existence of a class of exact local penalty functions (that is ones with a finite value of the penalty parameter) for a nonlinear programming problem. A lower bound to the penalty parameter is given by a norm of the optimal Lagrange multipliers which is dual to the norm used in the penalty function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588250
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 83
    Electronic Resource
    Electronic Resource
    Computational complexity of LCPs associated with positive definite symmetric matrices (1979)
    Springer
    Mathematical programming 17 (1979), S. 335-344 
    Details
    ISSN: 1436-4646
    Keywords: Linear Complementarity Problem ; Complementary Cones ; Complementary Pivot Methods ; Computational Complexity ; Exponential Growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Murty in a recent paper has shown that the computational effort required to solve a linear complementarity problem (LCP), by either of the two well known complementary pivot methods is not bounded above by a polynomial in the size of the problem. In that paper, by constructing a class of LCPs—one of ordern forn ≥ 2—he has shown that to solve the problem of ordern, either of the two methods goes through 2 n pivot steps before termination. However that paper leaves it as an open question to show whether or not the same property holds if the matrix,M, in the LCP is positive definite and symmetric. The class of LCPs in whichM is positive definite and symmetric is of particular interest because of the special structure of the problems, and also because they appear in many practical applications. In this paper, we study the computational growth of each of the two methods to solve the LCP, (q, M), whenM is positive definite and symmetric and obtain similar results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588254
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 84
    Electronic Resource
    Electronic Resource
    Call for papers: Second Symposium on Mathematical Programming with Data Perturbations (1979)
    Springer
    Mathematical programming 17 (1979), S. 398-399 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588258
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 85
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 17 (1979), S. 402-402 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588262
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 86
    Electronic Resource
    Electronic Resource
    The computation of Lagrange-multiplier estimates for constrained minimization (1979)
    Springer
    Mathematical programming 17 (1979), S. 32-60 
    Details
    ISSN: 1436-4646
    Keywords: Lagrange Multipliers ; Linearly-Constrained Optimization ; Augmented Lagrangian Functions ; Projected Lagrangian Methods ; Quadratic Sub Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Almost all efficient algorithms for constrained optimization require the repeated computation of Lagrange-multiplier estimates. In this paper we consider the difficulties in providing accurate estimates and what tests can be made in order to check the validity of the estimates obtained. A variety of formulae for the estimation of Lagrange multipliers are derived and their respective merits discussed. Finally the role of Lagrange multipliers within optimization algorithms is discussed and in addition to other results, it is shown that some algorithms are particularly sensitive to errors in the estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588224
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 87
    Electronic Resource
    Electronic Resource
    Glass cutting in a small firm (1979)
    Springer
    Mathematical programming 17 (1979), S. 85-90 
    Details
    ISSN: 1436-4646
    Keywords: Cutting Stock ; Glass Industry ; Approximate Solution ; Knapsack ; Small Firm ; Cutting Sequencing ; Small Order Size
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A description of some examples of the application of cutting stock problems is given. Focusing on a small firm and its special problems a case from the glass industry is presented. The case leads to a two-dimensional cutting stock problem where large rectangles have to be cut into smaller rectangles. At the same time a group of additional constraints have to be satisfied. The solution method is a near optimal method using knapsack functions. It is shown that the waste can be reduced by approximately 50% in comparison to the solution normally used by the company. Furthermore a sequencing procedure for the ordering of the glass sheets is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588227
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 88
    Electronic Resource
    Electronic Resource
    Piecewise linear paths to minimize convex functions may not be monotonic (1979)
    Springer
    Mathematical programming 17 (1979), S. 106-108 
    Details
    ISSN: 1436-4646
    Keywords: Fixed-point Algorithms ; Unconstrained Minimization ; Monotonic Paths
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The exact homotopy path when seeking the minimum of a convex function is monotonic in the homotopy parameter. This monotonicity is not inherited by the piecewise linear approximations to such paths produced by fixed-point algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588230
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 89
    Electronic Resource
    Electronic Resource
    Eleventh International Symposium for 1982 (1979)
    Springer
    Mathematical programming 17 (1979), S. 119-119 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588234
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 90
    Electronic Resource
    Electronic Resource
    On conditions for optimality of the nonlinearl 1 problem (1979)
    Springer
    Mathematical programming 17 (1979), S. 123-135 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinearl 1 Problem ; Nondifferentiable Functions ; Optimality Conditions ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to present necessary and sufficient conditions for optimality in the nonlinearl 1 problem. Furthermore, the relationship of thel 1 problem and the Pietrzykowski's approach to solve the nonlinear programming problem is discussed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588238
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 91
    Electronic Resource
    Electronic Resource
    Penalty methods for computing points that satisfy second order necessary conditions (1979)
    Springer
    Mathematical programming 17 (1979), S. 229-238 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Penalty Methods ; Second Order Necessary Conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Penalty methods using second derivatives are presented for computing points that satisfy second order necessary conditions for the constrained case in nonlinear programming. Convergence to such points is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588245
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 92
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 17 (1979), S. 248-248 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588248
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 93
    Electronic Resource
    Electronic Resource
    Acceleration of the leastpth algorithm for minimax optimization with engineering applications (1979)
    Springer
    Mathematical programming 17 (1979), S. 270-297 
    Details
    ISSN: 1436-4646
    Keywords: Minimax Optimization ; Nondifferentiable Optimization ; Computer-Aided Circuit Design ; Leastpth Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588251
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 94
    Electronic Resource
    Electronic Resource
    Updated triangular factors of the working basis in winkler's decomposition approach (1979)
    Springer
    Mathematical programming 17 (1979), S. 391-397 
    Details
    ISSN: 1436-4646
    Keywords: Decomposition ; Forrest-Tomlin Update ; Large Scale LP ; Linear Programming ; Triangular Factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588257
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 95
    Electronic Resource
    Electronic Resource
    The decomposition of nonlinear problems (1979)
    Springer
    Mathematical programming 17 (1979), S. 400-400 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588259
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 96
    Electronic Resource
    Electronic Resource
    On the lower semicontinuity of optimal sets in convex parametric optimization (1979)
    Springer
    Mathematical programming 17 (1979), S. 400-400 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588260
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 97
    Electronic Resource
    Electronic Resource
    On the width—length inequality (1979)
    Springer
    Mathematical programming 17 (1979), S. 403-417 
    Details
    ISSN: 1436-4646
    Keywords: Networks ; Graphs ; Resistor Networks ; Max-flow Min-Cut
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper was written at the Rensselaer Polytechnic Institute in 1963. A lecture based on it was given at the Rand Corporation in 1965 and this version is in the form in which Ray Fulkerson received it at Rand. The paper is the underpinning for results on resistor network inequalities (Reference [4]) which has not been published. A specific example, however, appears inProceedings of the IEEE 51 (1963) 1047–1048. There is also a parallel theory of the abstract assignment problem; every W—L matrix being an assignment matrix. More is known about minimal non-W—L matrices. U. Peled has found several additional classes of matrices which are also classically known in other contexts. A consequence of a recent matrix theorem is apparently that the degenerate projective planes are the only minimal matrices requiring unequal weights.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588263
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 98
    Electronic Resource
    Electronic Resource
    Set Partitioning mit linearen Randbedingungen (1979)
    Springer
    OR spectrum 1 (1979), S. 75-87 
    Details
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary An algorithm for solving the well-known Set-Partitioning-Problem with Side Constraints will be presented. The algorithm is of the Implicit Enumeration type and uses Subgradient Optimization for cost-transformation. A heuristic for partitioning the variables into blocks and a Fixing-Test based upon the Side Contraints are developed. Finally some details of Computer-Implementation and numerical test results are given.
    Notes: Zusammenfassung Es wird ein Algorithmus zur Lösung des bekannten Set-Partitioning-Problems mit Randbedingungen dargestellt. Der Algorithmus ist vom Typ der Impliziten Enumeration und benutzt Subgradientenoptimierung zur Kostentransformation. Eine Heuristik zur Zerlegung der Menge der Variablen in Blöcke sowie ein Fixierungs-Test basierend auf den Randbedingungen werden entwickelt. Abschließend sind einige Details der Computer-Implementation und numerische Testergebnisse aufgeführt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719072
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 99
    Electronic Resource
    Electronic Resource
    Production scheduling and sequencing for multi-stage production systems (1979)
    Springer
    OR spectrum 1 (1979), S. 103-114 
    Details
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In diesem Beitrag werden mehrstufige Mehrprodukt-Produktionssysteme mit dynamischem Zeitablauf betrachtet. Da die entsprechenden Modelle es erfordern, gleichzeitig Seriengröße und -folge zu bestimmen derart, daß ein zulässiger Produktionsplan erhalten wird, hat man sich bisher wenig mit solchen realistischen Problemen beschäftigt. Optimale und heuristische Lösungsverfahren für dieses kombinierte Entscheidungsproblem werden vorgestellt. Die Rechenerfahrungen deuten darauf hin, daß das vorgeschlagene heuristische Lösungsverfahren effektiv ist und die erreichten Lösungen sich von einer Optimallösung nur wenig unterscheiden.
    Notes: Summary This paper focuses on multistage, multiproduct dynamic production systems. Up to now little work has been done on such realistic problems, the reasons being that multiproduct models are subject to capacity considerations and to the general sequencing problem. Optimal and heuristic solution methods are presented for this combined sequencing/scheduling problem. Our computational experience indicates that the proposed heuristic is efficient and differs marginally from the optimal solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719074
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 100
    Electronic Resource
    Electronic Resource
    Lieferbereitschaft bei sporadischem Bedarf (1979)
    Springer
    OR spectrum 1 (1979), S. 115-122 
    Details
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary This paper is focused on a comparison of two methods for computing the reorder point when a certain service level is required: the first being suggested by Brown and implemented in Impact, the second to be found in a earlier article by the outhor. It is demonstrated by means of simulation that Brown's method doesn't reach the required service level when demand is lumpy. It turns out that the (s, S)-policy suggested in this paper yields much better the desired service level.
    Notes: Zusammenfassung Ein zentrales Problem bei der Lagerbewirtschaftung ist die Aufrechterhaltung einer vorgegebenen Lieferbereitschaft. In diesem Beitrag wird ein Lagerhaltungssystem mit periodischer Überprüfung des Lagers betrachtet. Für sporadischen Bedarf wird gezeigt, daß die in vielen Programmpaketen implementierte von Brown vorgeschlagene (s, Q)-Bestellpolitik in einem periodischen Überprüfungssystem zu einer erheblichen Unterschreitung des gewünschten Servicegrades führt, während eine (s, S)-Politik eine relativ gute Einhaltung des vorgegebenen Servicegrades garantiert.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719075
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...