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  • Springer  (24,865)
  • American Institute of Physics (AIP)
  • Institute of Electrical and Electronics Engineers (IEEE)
  • 2015-2019
  • 1965-1969  (24,865)
  • 1965  (24,865)
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  • 2015-2019
  • 1965-1969  (24,865)
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  • 1
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    Bulletin of mathematical biology 27 (1965), S. 49-63 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Compartmental systems can be represented by direct graphs in which each node corresponds to a generating function and each arm to a transfer generating function. A homomorphism is established between a compartmental system and this representation, in analogy with that obtained through the use of the Laplace transformation. From the values obtained experimentally in a given compartment, through the solution of a difference equation, the generating function for the corresponding node can be calculated and the graph of the system can be built up within the degrees of freedom of the model. From the graph it is possible to calculate the transfer generating function between any two connected nodes, the mean permanence time in a given node, the mean transit time between two nodes, and their precursor-successor order.
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  • 2
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    Bulletin of mathematical biology 27 (1965), S. 85-89 
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    Notes: Abstract The Competitive Exclusion Principle, formulated by V. Volterra (Memorie del R. Comitato Talassografico Italiano,131, 1–142, 1927) for a number of species competing for a common ecological niche, is extended to a number of species competing for many ecological niches.
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  • 3
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    Bulletin of mathematical biology 27 (1965), S. 65-70 
    ISSN: 1522-9602
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    Notes: Abstract A modification is presented of an earlier theory of the mixing of dye following injection into the circulation. Approximate theoretical relations are given for the concentration of dye in the right heart and in the aorta following right atrial injection. It is shown that when the probability distribution of transit times around the circulation has a prolonged tail, mixing waves are now inscribed about a quasi-exponential relation. Later in time the relation levels off to a uniform asymptotic concentration corresponding to an equilibrium volume of dilution.
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    Bulletin of mathematical biology 27 (1965), S. 91-104 
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    Notes: Abstract The adsorption of two cations at the anionic sites of a polymer (e.g., such as a protein) in an electric fields is discussed, taking into account cooperative interaction of the cations mediated through the backbone of the polymer. The calculation of the grand partition function explicitly considers the vacant negative sites of the polymer. As in the case without cooperative interaction, the problem reduces to the determination of the largest eigenvalue of asymmetric matrices. The weights of the different neighbor configurations are determined. Approximate formulae for the grand partition function and for those weights are derived. The formal analogy of these cooperative phenomena and those occurring in quantum (bio)chemistry is pointed out exemplifying an earlier suggestion about the basis of quantum biology.
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    Bulletin of mathematical biology 27 (1965), S. 105-112 
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    Notes: Abstract The transformation from gel to sol in cell cytoplasm is treated as the transition from a lattice of macromolecules linked by Ca++ ions to a random distribution of the macromolecules. The transition is a cooperative process, whose probability is expressed in terms of the theory of runs. The process is related to cell metabolism by the assumption that available Ca++ concentration is regulated by metabolically produced endogenous chelating agents.
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  • 6
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    Bulletin of mathematical biology 27 (1965), S. 113-118 
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    Notes: Abstract Kinetic criteria for solid state physical mechanisms of electron and ion transport in biological systems are summarized, and the mechanisms are discussed. A reaction which is rate-limited by electron or ion transport across a particle or membrane in accord with Ohm's law will show first order kinetics, with an hyperbolic relationship between rate constant and the sum of substrate plus product. Larger initial substrate concentrations produce smaller rate constants, thus giving the appearance of substrate inhibition. Examples are cytochrome oxidase and peroxidase, and pyruvate carboxylase. Ohmic transport mechanisms may be caused by electron conduction or superconduction through protein, by electron conduction through water, or by conduction of ions through membranes. A reaction which is rate-limited by charge transport across an activation energy barrier at an interface in accord with a logarithmic voltage-current law will show reaction kinetics conforming to the Elovich equation, and will have the appearance of a pair of simultaneous first order processes. Examples include decay of photogenerated free radicals in eye melanin particles and in photosynthetic particles of bacteria, and sodium and potassium ion transport across cell surfaces. The logarithmic voltage-current law may be regarded as an empirical relationship describing behavior of interfaces, justified by extensive experimental data on many types of interfaces, or it may be derived theoretically for individual cases from statistical mechanical and/or solid state physical considerations.
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  • 7
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    Bulletin of mathematical biology 27 (1965), S. 119-130 
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    Notes: Abstract When aortic pressure curves were predicted previously on the basis of a newly developed model of visco-elastic properties of the aorta, it was necessary to use published viscoelastic constants. These were usually obtained from longitudinal strips of blood vessels long removed from the animal, and therefore probably containing deteriorated smooth muscle. The predicted curves had the same form as actual tracings, substantiating the analysis somewhat, but the pressure levels were low. These low levels, if due to inadequate visco-elastic constants, could be attributed to the use of longitudinal rather than circumferential segments as well as to the use of segments with deteriorated muscle. The present analysis uses data collected by the author testing circumferential viscoelastic properties of fourteen different aortic regions in a way suggested by the author's model of an aortic wall. Moreover, the constants were measured on segments containing muscle relaxed by EDTA solutions and on similar segments containing muscle contracted by neosynephrine. These visco-elastic constants were used in the author's nonlinear differential equation of motion of the aortic wallin vivo to predictin vivo pressure curves. The predicted curves were low in any given aortic region if relaxed constants were used, but at normal levels with contracted constants. In fact, pressure curves predicted using constants obtained from aortic segments containing contracted muscle resembled actual tracings in form and pressure levels. Even the observed variations in the form of the systolic pressure curve down the aorta were predicted by this analysis.
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    Bulletin of mathematical biology 27 (1965), S. 131-133 
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    Notes: Abstract It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation $$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$ A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.
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    Bulletin of mathematical biology 27 (1965), S. 135-143 
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    Notes: Abstract C. Shannon's definition (Bell System Technical Journal,27, 379–423, 1948) of the entropy of a continuous distribution is dimensionally incorrect and does not have the same significance as the corresponding definition in the discrete case. A new definition is proposed: this modified entropy is more like the entropy of a discrete distribution in one way, in another more like Shannon's “transmission rate.” The ideas are illustrated by reference to Wright's study of the hereditary influence on the coat pattern of the guinea pig.
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    Bulletin of mathematical biology 27 (1965), S. 145-150 
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    Notes: Abstract In the following paper, a possible mode of evolution is described which differs from the traditional modes in not being selective in the Darwinian sense.
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    Bulletin of mathematical biology 27 (1965), S. 177-181 
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    Notes: Abstract A description of the kinds of systems susceptible to information theoretical analysis is given. By means of an example, certain common fallacies in the application of communication theory to biology are illustrated. The entropy-information analogy is discussed. *** DIRECT SUPPORT *** A01E2109 00008
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  • 12
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    Bulletin of mathematical biology 27 (1965), S. 161-175 
    ISSN: 1522-9602
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    Notes: Abstract A mathematical model of a process contains parameters supposedly characterizing the system which manifests the process. If the parameters are statistically distributed in a population of such systems, the process manifested by the entire population will in general be described by a different mathematical model. Thus a choice is always at hand between two or more mathematical models, depending on which parameters (if any) are assumed to be distributed and, if so, how. Examples of such alternative interpretations are given for mathematical models of some behavioral processes.
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    Bulletin of mathematical biology 27 (1965), S. 191-202 
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    Notes: Abstract The problem of economically linking a large number of stimuli with a large number of potential responses is considered to resemble a problem of efficient retrieval of documents (the responses) on the basis of their characterization by descriptors (the stimuli to which the responses are appropriate). In this retrieval problem, a method whereby the codes for descriptors are random positions in a coding field, and whereby codes for all applicable descriptors are superimposed in the same field, seems to be the simplest way of avoiding serious difficulties of retrieval. After a review of this method, the possibility is considered that very simple neural mechanisms could embody the essential features of the method. The aim of the discussion is to learn whether very simple structures and patterns of reinforcement would be adequate to carry out useful information processing in the brain, and to show some conceivable functions of simple neural networks which the experimenter might keep in mind. The discussion also shows how the structure of a simple “perceptron”-like network is suggested by the requirements of a retrieval task.
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    Bulletin of mathematical biology 27 (1965), S. 223-233 
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    Notes: Abstract A model is proposed to relate the regeneration of the ERGa-wave after partial light adaptation to the level of the light adaptation. The model assumes that thea-wave amplitude is a function of some reactive substance associated with ana-wave generator. The maximuma-wave amplitude occurs when the eye is fully dark adapted, and thea-wave generator initiator concentration is at a maximum. Thea-wave generator initiator concentration can be decreased by interacting with a product of the rhodopsin-light energy reaction, and increased by removal of this inhibitor. The removal of the inhibitor depends upon the isomerization of the all-trans-retinene to the 11-cis form. An excess of inhibitory material overa-wave generator initiator would cause a delay in the appearance of thea-wave until the excess inhibitory material is removed. This delay is a linear function of the logarithm of the adapting energy. The agreement of this model with the experimental ERG data is very good.
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    Bulletin of mathematical biology 27 (1965), S. 215-222 
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    Notes: Abstract The survival rate of fishes in their earlier stages of development and the influencing factors present one of the most fundamental problems of fish population dynamics. After I. Hjort's (Cons. L.'explor. Ner.,20, 3–228, 1914) work, there have been many investigators in this field and there is no doubt about the very important role of ova and larvae mortality in the fate of a given fish generation. Less clear are the ideas concerning factors determining the high mortality of fishes in their earlier stages of development; especially the factor of food supply of larvae during the period of transition to exogenic nutrition. The value of this factor has been estimated differently from different points of view. For example, R. J. H. Beverton and S. J. Holt (On the Dynamics of Exploited Fish Population, 1957) have given to the food supply factor its deserved importance. On the other hand, T. V. Dekhnik (Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960;Ibid.,14, 222–243, 1961) has proved in her investigations that at least for pelagic larvae of Black Sea fishes there is an excessive amount of food, and that therefore food cannot play an important role in larva survival. Not wanting to stop to review the literature of the problem (see Dekhnik,Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960), we will only remark that the problem as a whole needs further investigation. Not only new data are needed, but also methods for following up analysis have to be worked out.
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    Bulletin of mathematical biology 27 (1965), S. 253-259 
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    Notes: Abstract The investigation described here is anexperimental one which brings to light some new facts and confirms others already reported. They partly concern the hysteresis phenomena handled by N. Rashevsky (Mathematical Biophysics, 1960) and partly provide a point of departure for future biophysical research to be undertaken by biomathematicians.
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    Bulletin of mathematical biology 27 (1965), S. 27-52 
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    Notes: Abstract The aortic pressure curve necessarily reveals the mechanical properties of the aorta and peripheral resistance as well as of the dynamics of blood flow. The present study uses a reasonable model of visco-elastic properties of the aorta, a reasonable form for variations in peripheral resistance and blood flow to predict an aortic pressure tracing. Numerical values of constants measured experimentally were available in the published literature. These were used in the nonlinear differential equations of motion of the system under analysis. The equations yielded to piece-wise solution, giving the aortic circumference and the aortic pressure as functions of time. The form of both curves resembles clinical tracings, but numerical values of circumference were higher and of pressure lower thanin vivo. The discrepancies between predicted and clinical curves may reveal certain inadequacies in published measurements on visco-elastic constants. These measurements have been made on longitudinal rather than circumferential strips often containing dead rather than living muscle. The discrepancies, therefore, indicate specific gaps in our knowledge of aortic behaviorin vitro. The suggested model of the system aided in the design of experiments which could supply data necessary to substantiate or to revise the model.
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    Bulletin of mathematical biology 27 (1965), S. 373-377 
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    Notes: Abstract Some aspects of the circulation through the veins remain unexplained. The pressure gradient which ordinarily exists across a large vein, for example, is much greater than that necessary to maintain the same flow through a rigid tube of identical diameter (Brecher, 1956; Starling and Evans, 1962). During inspiration, blood flow through the thoracic portion of the inferior vena cava increases markedly, while that through the distal abdominal portion does not change. Furthermore, an active source of pressure drop in the chest is necessary to maintain venous flow. For the open chest the pressure drop occurs mainly during ventricular contraction, while in the closed chest it is produced chiefly by inspiration. The present study indicates that the high distensibility of the veins accounts in significant degree for the behavior characteristic of the venous circulation.
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    Bulletin of mathematical biology 27 (1965), S. 379-387 
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    Notes: Abstract This paper is an attempt to provide a logical model for the process of growth and differentiation in a multi-cellular organism. More specifically it is intended to show how genetic information relating to macroscopic structure and coded in the form of a logical tree could be progressively embodied in the organism as it develops by repeated division from a single cell. The aim is to establish biological analogies rather than mathematical interest, and reproduction, adaption, and the coordinating action of hormones are discussed within the general logical framework.
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    Bulletin of mathematical biology 27 (1965), S. 407-415 
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    Notes: Abstract Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.
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    Bulletin of mathematical biology 27 (1965), S. 389-406 
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    Notes: Abstract The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur.
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    Bulletin of mathematical biology 27 (1965), S. 431-434 
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    Notes: Abstract The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems.
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    Bulletin of mathematical biology 27 (1965), S. 417-429 
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    Notes: Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation: $$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB 1(t) is the first order initial entry function for the tracer material,P(t1) the perturbation function.T(t 2) is the tracer input function, andB 1(t−t 2 ,t 1 −t 2 ) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system.
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    Bulletin of mathematical biology 27 (1965), S. 435-447 
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    Notes: Abstract A correspondence is established between a tangible model of brain structure (and function) and a system of observer-observed interactions. The observed quantities are “stimuli” in the form of signal amplitude distributions in a mass of neuron-like units; the observer is a set of neurons (not circumscribed in a local region) in which a distributed parameter mirrors the stimulus history of the set, i.e., represents a “memory”. Utilizing the theory of the Perceptron, a contemporary brain model, it is demonstrated that large systems composed of many observer-observed interactions exhibit quantum mechanical behavior on a “macroscopic” scale. This behavior entails wave-like phenomena and the need of applying the superposition mechanics to system information content calculations.
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    Bulletin of mathematical biology 27 (1965), S. 449-471 
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    Notes: Abstract This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly.
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    Bulletin of mathematical biology 27 (1965), S. 473-476 
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    Notes: Summary Mathematical models of nonuniform gas distribution in the lungs which assume a two-chambered lung to be ventilated through a third chamber, i.e. a common dead space, have led to diverging results. A breath-by-breath analysis of such a system results in a two-exponential solution whereas a continuous ventilation analysis gives a three-exponential solution. This is caused by the different assumptions made in the two models about the composition of dead space gas. In the breath-by-breath analysis one assumes that theN 2 content of the dead space is zero at the end of inspiration. In the continuous ventilation model one assumes that theN 2 content in the dead space is unknown at all instants during the breathing cycle. No physical significance should be attached to any chamber in this type of analysis. The continuous ventilation model provides a more general solution than the cyclical ventilation model, because the former treats the common dead spaces as an independent unknown.
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    Bulletin of mathematical biology 27 (1965), S. 493-495 
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    Bulletin of mathematical biology 27 (1965), S. 477-491 
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    Notes: Abstract The different approaches to relational biology developed by N. Rashevsky and R. Rosen consider essentially binary relations between various components of biological functions of the organism. Actually an organism is represented by a set of differentn-ary relations. The present paper is an attempt to outline a possible approach to this more realistic situation. Inasmuch asn-ary relation is ann-place predicate, it is attempted to describe the basic known properties of an organism in terms ofn-place predicates, in which the variables represent the different “components” of the organism. Some possible forms of such predicates are discussed and some general properties of systems of such predicates are studied. It is shown that if the organism is described by predicates of the type discussed here, statements can be derived about the conditions “of reestablishability” of different components. Conclusions similar to those obtained previously by R. Rosen are reached now on a very different basis. A description of the process of cell differentiation in multicellular organisms in terms of predicates studied here is briefly outlined. A comparison of similarities and differences between the approach and Rosen’s description of organisms in terms of the theory of categories is made.
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    Bulletin of mathematical biology 27 (1965), S. 497-500 
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    Bulletin of mathematical biology 27 (1965), S. 503-503 
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    Bulletin of mathematical biology 27 (1965), S. 501-502 
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    Bulletin of mathematical biology 27 (1965), S. 57-65 
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    Notes: Abstract An outline is given of an analysis that leads to an exact solution for the problem of steady-state diffusion through a finite thick pore into an infinite region surrounding the mouth of the pore. From this exact formula a simple expression for the flux is derived. This expression approximates the flux with a relative error of less than 3.42 per cent independently of the ratiol/a wherel is the length of the pore anda its radius. If desired, more accurate expressions for the flux can be obtained from the exact solution.
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    Bulletin of mathematical biology 27 (1965), S. 79-86 
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    Notes: Abstract The model proposed by A. L. Hodgkin and R. D. Keynes (Jour. of Physiol.,128, 61–88, 1955) for the diffusion of potassium through the nerve membrane is extended to cover an arbitrary number of species of ions with charges not necessarily the same. One type of interference is also investigated.
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    Bulletin of mathematical biology 27 (1965), S. 71-83 
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    Notes: Abstract Most theoretical studies of the circulation have focussed on the transmission line properties of arteries. Only a small number of papers have dealt with the circulation as a closed (lumped) system with two pumps connected by the lesser and greater circulation (Beneken, inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Defares,et al., inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Grodins,Quart. Rev. of Biology,34, 93, 1959; Guyton,Cardiac Output and its Regulation, Saunders Publ. Co., New York, 1963). F. W. Cope's recent studies in this journal (Bull. Math. Biophysics,22, 19, 1960;23, 337, 1961;24, 137, 1962) deal with essentially the same questions, although here the circuit is not “closed”. We have attempted to extend the analysis of the areflex (closed) circulation. The complete study is reported elsewhere (Defares,et al., Acta Physiol, et Parmac. Neerl., 1963).
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    Bulletin of mathematical biology 27 (1965), S. 67-78 
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    Notes: Abstract A vector integral equation describing heat distribution within the body has been derived. The factors considered are heat conduction, forced convection via the circulatory system, environmental exchange, metabolic heat production, and change in heat content. The vector partial differential equation and alternative forms incorporating boundary conditions were also developed. A difference equation based on a first-order approximation to the fundamental equations was derived to form the basis of a model for heat distribution within the body. It has been shown that factors involving conduction and convection must be considered independently unless the temperature of the blood flowing from a region of the body is equal to the average temperature of the tissue in that region. If this relation between tissue and blood temperature does exist, only a single temperature from each eleeent is needed to describe the heat distribution. In this latter case, models which ascribe all heat transfer to “equivalent” conduction or to convection can give valid predictions.
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    Bulletin of mathematical biology 27 (1965), S. 87-98 
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    Notes: Abstract It is shown that in a system containingn types of mutually noninteracting binding sites, the association constants are then roots of annth order polynomial while the maximum binding capacities can be evaluated by solving a set ofn simultaneous linear equations. Thenth order polynomial and the system ofn linear equations are defined in terms of 2n intermediate coefficients, the coefficients being themselves evaluated by substituting 2n sets of appropriate experimental data into an auxiliary system of 2n linear equations. The existence and uniqueness of the solutions are established.
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    Bulletin of mathematical biology 27 (1965), S. 111-111 
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    Bulletin of mathematical biology 27 (1965), S. 113-113 
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    Bulletin of mathematical biology 27 (1965), S. 99-109 
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    Notes: Abstract A kinetic theory of ion transport across cell surfaces has been developed in a form analogous to the kinetic theory of electron transport across solid-liquid interfaces of biological particles. The ionic theory is based on the observation that, at least in one instance, the voltage-current behavior for ion conduction across a cell surface is describable by the Tafel equation, in analogy to the conduction of electrons across solid-liquid interfaces. The theory predicts that the kinetics of ion transport across cell surfaces should conform to the Elovich rate equation, which is shown to be true for various experimental data.
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    Bulletin of mathematical biology 27 (1965), S. 114-114 
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    Bulletin of mathematical biology 27 (1965), S. 115-115 
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    Bulletin of mathematical biology 27 (1965), S. 3-4 
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    Bulletin of mathematical biology 27 (1965), S. 5-10 
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    Bulletin of mathematical biology 27 (1965), S. 11-14 
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    Notes: Abstract The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an (ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958.
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    Bulletin of mathematical biology 27 (1965), S. 21-37 
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    Notes: Abstract A simplified, linearized model of the system regulating blood-glucose concentrations is reviewed. This model, which predicts a damped sine wave response to an oral glucose load, lumps the large number of kinetic parameters into a much smaller number which can, at least in part, characterize the human glucose regulatory system. The predictions based on the model are compared with measurements of blood-glucose and blood-insulin concentrations during the oral glucose-tolerance test. Various other conditions are simulated and their implications are discussed in terms of the mathematical model used.
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    Bulletin of mathematical biology 27 (1965), S. 15-19 
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    Notes: Abstract The notion of a compartment is discussed in terms of the Markovian process. From the stochastic matrix (the elements of which are state transition probabilities between different states of a particle of a chemical element), one may find a (generally) nonstochastic matrix; the elements of this second matrix are probabilities that, starting from some initial state, the particle will reach another seleced state (W. Feller, 1962,An Introduction to Probability Theory). Forming equivalence classes of states it can be shown that the equivalence classes based on an equivalence relation, which holds for the elements of the above-mentioned nonstochastic matrix, are essential for the notion of a compartment. From this procedure it is also obvious that a rigorous definition of a physically realizable compartment is impossible. Some conclusions on the practical use of compartmental analysis are drawn.
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    Bulletin of mathematical biology 27 (1965), S. 39-48 
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    Notes: Abstract In a population of cells labeled with a single injection of tritiated thymidine at timet=0, it is assumed that a constant fraction, 1−z, of the cells which are potentially able to divide fail to do so, and that the cells which do divide all have identical generation time,D. Death and emigration of cells are neglected. In mitosis, the partitioning of label among the two daughter cells is supposed to follow the binomial probability law. Using the formalism developed by H. Von Foerster the fraction of labeled cells in the total population is computed as a function oft, the time after injection of label. Ift is an integral multiple ofD the results coincide with those of S. A. Tyler and R. Baserga.
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    Bulletin of mathematical biology 27 (1965), S. 151-160 
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    Notes: Abstract A society with a dominance relation is considered to be built up by starting with a small society and adding new members in succession. As each member is added he engages in contests with each of the older members to determine the dominance relation between them. The probability that the older member dominates is considered to depend on the size of the society and linearly on the older members score. A recurrence relation for the hierarchy index is derived. The approach of the society to a hierarchical structure is considered for various special cases of this probability. Reasonable assumptions concerning this dominance probability are shown to lead to structures close to the hierarchy. If the new member dominates all the older ones below a certain rank, and is dominated by all those above this rank, then the hierarchy will persist if it is the initial structure, or the structure will tend to hierarchy as the size increases, if it is not the initial structure.
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    Bulletin of mathematical biology 27 (1965), S. 183-190 
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    Notes: Abstract The transport of oxygen in a hemoglobin-saturated medium is theoretically investigated using classical transport theory. It is found that all the chemical complexes can be expressed as a single function of oxygen pressure. A potential difference together with apH shift is predicted to occur across the medium.
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    Bulletin of mathematical biology 27 (1965), S. 203-214 
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    Notes: Abstract Several physical effects (magnetomotive force on ions, magnetic induction of electrical field, magnetic changes of inductance) are quantitatively analyzed in an attempt to attain an insight on how externally applied static magnetic fields influence the activity of the neuron and the Nervous System as a whole or in part. The possible magnetic action on shifting excited zones of the axon appears as most promising for prediction and interpretation of measurable effects. Magnetic fields may modify nervous functions by multiplication and addition of very small biophysical effects.
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    Bulletin of mathematical biology 27 (1965), S. 235-251 
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    Notes: Abstract In an earlier paper (Molecular Set Theory: I.Bull. Math. Biophysics,22, 285–307, 1960) the author proposed a “Molecular Set Theory” as a formal mathematical meta-theoretic system for representing complex reactions not only of biological interest, but also of general chemical interest. The present paper is a refinement and extension of the earlier work along more formal algebraic lines. For example the beginnings of an algebra of molecular transformations is presented. It also emphasizes that this development, together with the genetical set theory of Woodger's and Rashevsky's set-theoretic contributions to Relational Biology, points to the existence of a biomathematical theory of sets which is not deducible from the general mathematical, abstract theory of sets.
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    Bulletin of mathematical biology 27 (1965), S. 261-273 
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    Notes: Abstract Systems in which a human subject interacts with an adaptive control mechanism through display and response facilities are examined. A cybernetic model is discussed, together with supporting experimental data.
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    Bulletin of mathematical biology 27 (1965), S. 275-290 
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    Notes: Abstract Computer simulation of the stem-cell system has been motivated by a desire to provide a device which may assist the experimenter in his development of complex research strategies in the rapidly developing investigative fields that relate to erythropoiesis and granulopoiesis. A simulation program, written in FORTRAN II for the IBM-7094, is being developed with the requirements of flexibility and broad applicability in mind. The biological model for which it originally was developed differs from those previously advanced by visualizing differentiation into the erythrocytic and granulocytic series as occurring during the post-mitotic phase of a stem cell's growth, the cell's susceptibility to erythropoietic and granulopoietic stimuli varying as its biochemical development unfolds. One might test this model by attempting to demonstrate an asymmetrical interference between erythropoietic and granulopoietic challenges to the stem-cell system. A method for establishing an initial stable configuration of the model is presented. The simulation of the introduction of exogenous erythropoietic stimuli is described. And there is a brief description of the feedback mechanism employed to stabilize the size of the stem-cell population.
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    Bulletin of mathematical biology 27 (1965), S. 305-310 
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    Notes: Abstract In a system as complex and as effective as the eye, the cooperative interaction of different mechanisms may be taken as axiomatic. With this as a starting point, various visual phenomena are considered, such as short term memory, eye movements, and flicker fusion. Simple data on mean values lend support to the proposition that the spatial and temporal characteristics of these phenomena are matched with one another. The significance of this for a mechanism of vision is discussed.
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    Bulletin of mathematical biology 27 (1965), S. 311-315 
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    Notes: Abstract Matrix algebra is the natural tool for the study of linear stochastic models with many parameters. Complete solutions are given for the nonconfluent and the general confluent cases. It is shown that the axiomatics of a generalized linear stochastic model are naturally described within the framework of the linear algebra in an Euclidean space.
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    Bulletin of mathematical biology 27 (1965), S. 291-303 
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    Notes: Abstract An arbitrary set of chemical reactions is considered to occur among chemical speciesX i . In a closed uniform reaction system certain linear combinations of the concentrations of theX i are constants. The general construction of all such linear combinations with non-negative coefficients is given in terms of the molecular formulae for theX i . It is shown that to each such linear combination there corresponds another which is a harmonic function when the reactions take place in an open spatially distributed stationary reaction system of arbitrary shape. Under the usual boundary conditions these harmonic functions are constants. With some restrictions upon the diffusion and permeability coefficients these constants are evaluated. This evaluation is the basis for relations between the total concentration of a given chemical group (e.g., the sum of the concentrations of a free molecule, or ion, and its various bound forms) in the reaction system, and in the surrounding medium. The bearing of these relations on apparent active transport is noted and illustrated.
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    Bulletin of mathematical biology 27 (1965), S. 329-332 
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    Notes: Abstract It is shown that the partitioned initial entry functions previously introduced in multicompartment analysis can be directly and uniquely determined from the experimental data.
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    Bulletin of mathematical biology 27 (1965), S. 317-328 
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    Notes: Abstract An escape learning situation is discussed in terms of a neural model in which a stimulus can result in a conditioned excitement and a specific conditioned response. By using the simplest relations between the strengths of conditioning and the number of reinforcements and by introducing a distribution of fluctuations occurring regularly in time, one can calculate the probabilities of various responses, as well as the various latencies, in successive trials. The results are in moderately satisfactory agreement with the data of R. L. Solomon and L. C. Wynne (Psychol. Monogr.,67, No. 4, 1953). Consequences of the model for various experimental situations are discussed.
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    Bulletin of mathematical biology 27 (1965), S. 1-8 
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    Notes: Abstract Collateral circulation minimizes the myocardial injury which results from narrowing of a coronary artery. A large collateral circulation has disadvantages, however. It may divert so much of the limited blood flow through the adjacent nonarteriosclerotic coronary artery that the blood supply of the normal muscle supplied by that artery may be inadequate during heavy exercise. In the presence of a large collateral circulation, both the normal and ischemic regions of the heart may be extremely vulnerable to small arteriosclerotic changes narrowing the patent artery near the aorta. The effective increase in flow which results from arteriolar vasodilatation produced by drugs may be much greater in the presence of a small collateral circulation than a large one.
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    Bulletin of mathematical biology 27 (1965), S. 9-20 
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    Notes: Abstract A transfusion can be hypothesized to be required when a determination factor (D=probability of adverse effects if transfusion not given/adverse effects if transfusion is given) exceeds some predetermined value.D varies between the limits 0 and ∞, and in most clinical situations will be a small number on the order of 20. Since the probabilities contributing to the denominator ofD are essentially independent of each other, they can be summed to obtain the probability of ill effects. A method of handling an exception to this, the incompatibility reactions following multiple transfusions within a short time interval, is pointed out. The probability of adverse effects if a transfusion is not given is more difficult to evaluate; values gathered from the literature are presented, as well as methods for obtaining further data. Two techniques for estimating future transfusion requirements are discussed. One is a correlative procedure, which functions by analyzing similar cases admitted to the hospital. The second procedure is an estimate of stability (homeostasis), based on a parameter introduced by B. C. Patten (Scince,134, 1010–1011, 1961). The dilution of endogenous cells and plasma by transfusions is considered and the consequences of many small transfusions compared with those of few (and larger) transfusions.
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    Bulletin of mathematical biology 27 (1965), S. 21-26 
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    Notes: Abstract In continuation of a previous paper (Bull. Math. Biophysics,26, 167–185, 1964) simple equations are derived for the rate of development of schizophrenia as a function of some psychobiological parameters of the individual and of an index which characterizes the frequency of traumatic experiences of the individual. A clue to the understanding of why schizophrenia is more likely to develop at an early adult age is thus provided.
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    Bulletin of mathematical biology 27 (1965), S. 53-56 
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    Notes: Abstract A mathematical analysis is presented which shows that during stop flow experiments longitudinal diffusion of solute along the nephron is of too small a magnitude to interfere with the interpretation of data.
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    European journal of wildlife research 11 (1965), S. 121-135 
    ISSN: 1439-0574
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary 16 pairs of hawk out of the Northern German territory were investigated according to views of biological dietetics. It was shown that in the surroundings of Berlin the house pigeon is the prey preferred. In the Northern German inland regions Corvidae (jays, magpies, crows) as well as squirrels and rabbits are forming the basis of nutrition. The hawks of the Baltic sea coasts prefer water fowls (ducks and gulls). In the nutrition of the young thrushes, starlings, chaffinches, and other small birds, which the male hawk takes to the eyrie, play an important part. The adult hawks prefer for themselves always bigger prey. The small damage caused by hawks to shooting was in all cases balanced by the Corvidae, rabbits, and squirrels slain.
    Abstract: Resumé 16 couples d'autours pris sur la territoire de l'Allemagne du Nord furent examinés de façon bio-nutritive. Cet examen faisait voir que—aux environs de Berlin—le pigeon domestique était l'animal de proie préféré. Dans l'intérieur de l'Allemagne du Nord les corvidés (geais, pies, corneilles) ainsi que l'écureuil et le lapin constituent la base de l'alimentation. Les autours habitant la côte de la mer Baltique s'attaquent en premier lieu aux oiscaux aquatiques (canards et mouettes). Pour la nourriture des jeunes, les grives, étourneaux, pinsons et autres menus oiseaux que l'autour mâle rapporte au nid jouent un rôle important. Les vieux autours préfèrent pour leur besoin personel, une plus grande proie. Les dégâts de chasse peu importants, occasionnés par les autours examinés, furent égalisés dans tous les cas par les oiseaux corbeaux, lapins et écureuils capturés.
    Notes: Zusammenfassung 16 Habichtspaare aus dem norddeutschen Raum wurden ernährungsbiologisch untersucht. Es zeigte sich, daß in der Umgebung von Berlin die Haustaube das bevorzugte Beutetier ist. Im norddeutschen Binnenland bilden Rabenvögel (Eichelhäher, Elstern, Krähen) sowie Eichhorn und Wildkaninchen die Grundlage der Ernährung. Bei den Habichten der Ostseeküste stehen Wasservögel (Enten und Möwen) an erster Stelle. In der Ernährung der Jungen spielen Drosseln, Stare, Buchfinken und andere Kleinvögel, die vom männlichen Habicht an den Horst gebracht werden, eine wichtige Rolle. Für den Eigenbedarf der alten Habichte wird durchweg größere Beute bevorzugt. Der geringe jagdliche Schaden der untersuchten Habickte wurde in allen Fällen durch die erbeuteten Rabenvögel, Kaninchen und Eichhörnchen ausgeglichen.
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    European journal of wildlife research 11 (1965), S. 155-158 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Meteorology and atmospheric physics 15 (1965), S. 32-45 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Summary Two cases of invasions of cold air into the Alpine region which have occurred in April 1962 are investigated. The polar air intruded from the north with a vertical extension up to 2500 m on the frontside of an upper trough. The Tiros observations combined with the synoptic and aerological data permitted to generalize a formerly derived formula valid for upper troughs for cold fronts [4]. It could be shown that the cold front caused bad weather as well north of the Alps as south of them when it passed below the frontside of the upper trough. Closed systems of clouds at cold fronts orginate more probably at the front of troughs than at their backside, where downstreams perforate the cloud cover.
    Abstract: Résumé On examine ici le comportement de deux invasions d'air froid d'origine polaire qui se sont manifestées dans les Alpes en avril 1962. L'air polaire a pénétré dans la région des Alpes en venant du nord. Il avait une épaisseur de 2500 m et se déplaçait à l'avant d'un couloir dépressionnaire en altitude. Les observations du satellite météorologique “Tiros” combinées aux valeurs synoptiques et aérologiques permettent de généraliser une règle établie précédemment, règle qui concerne les fronts froids liés à des couloirs dépressionnaires en altitude [4]. Il en résulte que le front froid, en franchissant la partie antérieure d'un couloir, provoque un temps maussade aussi bien au nord qu'au sud des Alpes. Des systèmes nuageux compactes se forment en général de préférence à l'avant des couloirs dépressionnaires en altitude, car, à l'arrière de ceux-ci, les mouvements de subsideance qui y règnent provoquent des trouées dans la nappe nuageuse.
    Notes: Zusammenfassung Es werden zwei im April 1962 in den Alpen sich auswirkende polare Kaltlufteinbrüche untersucht. Die Polarluft drang von Norden her in den Alpenraum mit einer vertikalen Erstreckung bis zu 2500 m ein, und zwar an der Vorderseite eines Höhentroges. Die Tiros-Beobachtungen, kombiniert mit den synoptischen und aerologischen Meßdaten, erlaubten eine Verallgemeinerung einer früher abgeleiteten Höhentrogregel für Kaltfronten [4]. Es ergab sich, daß beim Unterlaufen der Höhentrog-Vorderseite die Kaltfront sowohl an der Alpennordseite als auch an der Alpensüdseite Schlechtwetter verursacht. Geschlossene Wolkensysteme an Kaltfronten entstehen ganz allgemein eher an der Trogvorderseite als an der Trogrückseite, wo absteigende Luftbewegungen die Wolkendecke durchlöchern.
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    Meteorology and atmospheric physics 15 (1965), S. 50-61 
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Der Zusammenhang zwischen der mittleren vektoriellen Windscherung und dem Scherungsintervall wird analysiert. Dabei kann gezeigt werden, daß diese Beziehung von der Erhaltungsneigung (Persistenz) der Scherungsvektoren mit dem Intervall abhängt. Dasselbe gilt für die Beziehung der Streuungen mit dem Scherungsintervall. Die Persistenz nimmt bei zunehmendem Scherungsintervall nach einem exponentiellen Gesetz ab. Daraus läßt sich ein Exponent für den oben erwähnten und vom Autor an anderer Stelle [7] abgeleiteten Zusammenhang zwischen mittlerer vektorieller Windscherung und Scherungsintervall von ungefährt 1/2 berechnen. Für Extremwerte scheint dagegen der Exponent um 1/3 zu liegen. Dies mag damit erklärt werden, daß Abweichungen von der zweidimensionalen normalen zirkulären Verteilung auftreten, die exponentiell mit wachsendem Scherungsintervall abnehmen und somit den Exponenten verkleinern.
    Abstract: Résumé On analyse ici la relation existant entre le cisaillement vectoriel moyen du vent et l'intervalle en altitude de ce cisaillement. On peut ainsi démontrer que cette relation dépend de la persistance du vecteur de cisaillement avec l'intervalle. Il en va de même de la relation entre la dispersion et l'intervalle de cisaillement. La persistance diminue exponentiellement avec l'augmentation de l'intervalle. On peut calculer un exposant d'environ 1/2 pour la relation mentionnée plus haut et déduite d'autre par par le même auteur [7]. Dans des cas extrèmes, cet exposant est d'à peu près 1/3. Cela peut être expliqué par le fait que l'on rencontre des écarts de la répartition normale circulaire à deux dimensions. Ceux-ci diminuent exponentiellement avec l'accroissement de l'intervalle de cisaillement et font, par conséquent, diminuer la valeur de l'exposant.
    Notes: Summary The relationship between the mean of the vector shears and the shear interval is analyzed and linked to the persistence of vector shears with the shear interval. A similar relationship exists between the standard deviation of the vector shears and the shear interval. As the persistence follows an exponential law, decreasing reciprocally with the shear interval, the relationship between mean vector shears and the shear interval Δh assumes a power law with exponent around 1/2. The exponent of 1/3 found in relationships between extreme values and shear interval may be attributed to deviations of the frequency distribution of vector shear values from the bivariate circular distribution.
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    Meteorology and atmospheric physics 15 (1965), S. 109-117 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary Observations with a RHI radar show that the so-called bright band, which is a layer of especially strong radar reflectivity, is only to be seen during the dissipating stage of convective precipitation cells (showers, thunderstorms). During the developing and mature stage of the cells one cannot observe the bright band.
    Abstract: Résumé Des relevés radar faits au moyen d'un appareil RHI montrent que l'apparition qu'il est convenu d'appeler «bright band» ne s'observe qu'au moment de la désagrégation de cellules convectives de précipitations (averses ou orages). La «bright band» est une couche dans laquelle la réflexion radar est spécialement intense. Si les dites cellules sont en formation ou bien développées, on n'observe par contre pas de «bright band».
    Notes: Zusammenfassung Radarbeobachtungen mit einem RHI-Radargerät zeigen, daß das sogenannte Bright Band, eine Schicht besonders starker Radar-Reflektivität, nur im Auflösungsstadium konvektiver Niederschlagszellen (Schauer, Gewitter) zu beobachten ist. Im Bildungs- und Reifestadium der Zellen wird das Bright Band nicht beobachtet.
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    Meteorology and atmospheric physics 14 (1965), S. 279-299 
    ISSN: 1436-5065
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    Description / Table of Contents: Zusasmmenfassung Es werden die Änderungen der thermischen Struktur der Luftmassen im Alpengebiet und im westlichen Mittelmeerraum bei der Entwicklung von Zyklonen im Golf von Genua aufgezeigt und die Einflüsse von Höhe und Form der Gebirgszüge sowie von nichtadiabatischen Vorgängen auf die Deformation der relativen Topographie besprochen. Diese Faktoren werden auch zur Modifikation der in der Methode vonEstoque für ein baroklines Modell verwendeten Gleichungen in Betracht gezogen und damit wird eine neue Methode zur Vorhersage der Zyklogenese unter dem Einfluß von Gebirgszügen entwickelt.
    Abstract: Résumé On expose dans ce mémoire à quelles modifications la structure thermique des masses d'air est soumise dans la région des Alpes et dans le bassin occidental de la Méditerranée lors du développement de dépressions sur le Golfe de Gênes. On y discute en outre l'influence de la hauteur et de la forme des chaînes de montagnes ainsi que celle des processus non-adiabatiques sur des déformations de la topographie relative. Tous ces éléments sont pris en considération pour leur adapter les équations utilisées dans le modèle baroclined'Estoque. Par là, on accède à une nouvelle méthode de prévision de la cyclogénèse, méthode qui tient compte de l'influence des chaînes de montagnes.
    Notes: Summary Changes occurring in the thermal structure of air masses in the Alps area and the West Mediterranean region, during cyclonic developments in the Gulf of Genoa, have been considered. The effect of the height and the form of the mountain ranges as well as that of the nonadiabatic processes, on the deformation of the thickness pattern, have been discussed. These factors have been further taken into consideration for a modification of the equations used inEstoque's method for the baroclinic model, and a new method has been developed for forecasting cyclogenesis in regions bounded by mountain ranges.
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    Meteorology and atmospheric physics 14 (1965), S. 300-305 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Summary Making use of a statistical theory developed byK. Cehak probabilities are given for the occurrence of maxima of wind velocity of given amount and minimum-amount. This is done on the base of informations about the spectral density distribution of the kinetic energy of the wind.
    Abstract: Résumé Partant d'une théorie statistique développée parK. Cehak, l'auteur calcule les probabilités d'apparition de vents maximum. Pour ce faire, il se sert d'informations touchant la répartition spectrale de la densité d'énergie cinétique du vent. Les dites probabilités sont en outre établies pour quelques valeurs totales et pour des grandeurs minimum admises préalablement.
    Notes: Zusammenfassung Nach einer vonK. Cehak entwickelten statistischen Theorie werden mittels Informationen über die spektrale Dichteverteilung der kinetischen Energie des Windes Wahrscheinlichkeiten für das Auftreten von Geschwindigkeitsmaxima von vorgegebener Größe und Mindestgröße angegeben.
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    Meteorology and atmospheric physics 14 (1965), S. 318-342 
    ISSN: 1436-5065
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    Description / Table of Contents: Zusammenfassung Es wird ein neues Modell für ein Spektrometer zur Bestimmung der Ionenbeweglichkeit beschrieben, das auf den wesentlichen Konstruktionseigenschaften des Kernzählers vonPollak undNolan beruht. Es wird zur Analyse der Größenverteilung eines künstlichen Aerosols von Aitken-Kernen in verschiedenen Zerfallstadien benützt. Das Instrument hat sich in seiner ersten Ausführung als recht befriedigend erwiesen, und es werden Anregungen für seine Verbesserung diskutiert.
    Abstract: Résumé L'auteur présente un nouveau modèle de spectromètre pour la mesure de la mobilité des ions. Cet appareil est basé sur les propriétés de conception du compteur de noyaux dePollak etNolan. Il s'emploie pour analyser la répartition des grandeurs d'un aérosole artificiel comprenant des noyaux de Aitken à différents stades de décomposition. L'instrument est tout à fait satisfaisant dans sa forme originale et l'on présente différentes suggestions pour l'améliorer encore.
    Notes: Summary A novel form of ionic mobility spectrometer is described, based on the intrinsic properties of the construction of thePollak-Nolan nucleus counter. It is used for the size-frequency analysis of an artificial aerosol of Aitken nuclei at various stages in its decay. The first, construction of the instrument has been found to perform quite satisfactorily; suggestions for its improvement are discussed.
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    Meteorology and atmospheric physics 14 (1965), S. 361-379 
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    Description / Table of Contents: Zusammenfassung Die sphärische harmonische Analyse der 24stündigen Bodenluftdruckschwankung zeigt, daß ihr Hauptteil durch eine mit der Sonne westwärts wandernde Welle dargestellt werden kann. Die Amplitude dieser Welle ist ungefähr die Hälfte der 12stündigen Schwankung [Gleichung (7)]. Zur Diskussion der thermischen Erregung der 24stündigen Schwankung wurden die äquivalenten Tiefen (Tabelle 4) und Hough-Funktionen (Tabellen 5, 6) für die drei niedrigsten symmetrischen Typen berechnet. Es besteht keine Schwierigkeit, auf Grund der Theorie der thermischen Erregung zu erklären, warum die 24stündige Schwankung viel kleiner ist als die 12stündige, selbst wenn die letztere nicht bedeutend durch Resonanz vergrößert wird.
    Abstract: Résumé L'analyse harmonique sphérique des variations de pression au sol en 24 heures montre que sa partie principale peut être repés entée par une onde se propageant vers l'ouest avec le soleil. L'amplitude de cette onde est d'à peu près la moitié de la variation en 12 heures [équation (7)]. Pour la discussion de la stimulation thermique de la variation en 24 heures, on a calculé les dépressions équivalentes (tableau 4) ainsi que les fonctions de Hough (tableux 5 et 6) et cela pour les trois types de symétrie les plus bas. En se basant sur la théorie de la stimulation thermique, il n'est pas di fficile d'expliquer pourquoi les variations en 24 heures sont beaucoup plus faibles que celles se produisant en 12 heures, même si ces dernières ne sont pas notablement renforcées par des effects de résonance.
    Notes: Summary A spherical harmonic analysis of the diurnal surface pressure oscillation shows that its main part can be represented by a wave travelling westward with the sun. The amplitude of this wave is about half of that of the semidiurnal oscillation [eq. (7)]. For the discussion of the excitation of the diurnal oscillation the equivalent depths (Table 4) and Hough functions (Table 5, 6) for the three lowest symmetrical modes are computed. There is no difficulty in accounting for the smallness of the diurnal oscillation compared to the semidiurnal oscillation on the basis of thermal excitation, even if the semidiural oscillation is not greatly magnified by resonance.
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    Meteorology and atmospheric physics 14 (1965), S. 409-419 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Summary The dependency of the speed of the zonal wind in the 850mb surface in one latitude on the speed in another latitude can qualitatively be compared with a model atmosphere according toRossby. With preservation of the angular momentum and the absolute vorticity a decrease of the zonal wind speed must occur in high latitudes when the zonal wind speed increases in low latitudes and vice versa. Further, it can be shown that the index cycle in the sense ofRiehl, Namias orDefant, and with it the zonal windprofile itself are less suitable for being used in the weather service as additional help in making medium range forecasts.
    Abstract: Résumé La dépendance entre la vitesse du vent zonal trouvée à 850 mb à une certaine latitude et celle d'une autre latitude peut être comparée — qualitativement — au modèle d'atmosphère selonRossby. Du fait de la persistance du moment absolu de l'impulsion et des échanges du moment tourbillonnaire absolu, il faut qu'à une augmentation de la vitesse du vent zonal dans les basses latitudes corresponde une diminution de cette vitesse aux latitudes élevées, et vice versa. Il en résulte en outre que le cycle des index, p. ex. dans le sens des définitions deRiehl, Namias ouDefant, — et par voie de conséquence les profils de vents zonaux eux-mêmes — s'avèrent inadéquats pour leur utilisation par les services métérologiques comme auxiliaires supplémentaires pour la prévision à moyenne échéance.
    Notes: Zusammenfassung Die Abhängigkeit der zonalen Windgeschwindigkeit in einer geographischen Breite von der in einer anderen Breite, wie sie für das 850 mb-Niveau gefunden wurde, kann qualitativ mit den Modellvorstellungen vonRossby verglichen werden. Aus der Erhaltung des absoluten Impulsmomentes und der absoluten Vorticity folgt bei einer Zunahme der zonalen Windgeschwindigkeit in niedrigen Breiten eine Abnahme in höheren Breiten und umgekehrt. Es ergibt sich ferner, daß sich der Indexzyklus im Sinne vonRiehl, Namias oderDefant und damit auch die zonalen Windprofile selbst für eine Verwendung im Wetterdienst als zusätzliches Hilfsmittel für mittelfristige Prognosen als nicht sehr geeignet erweisen.
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    Meteorology and atmospheric physics 14 (1965), S. 441-448 
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    Topics: Geography , Physics
    Description / Table of Contents: Summary The investigation of single cases shows that the horizontal extension of shower cells depends on the vertical wind distribution. The more the wind increases with height, the larger is the perimeter of the shower cell.
    Abstract: Résumé L'examen de cas isolés montre que le diamètre horizontal des cellules de précipitations sous forme d'averses dépend en grande partie de la répartition des vents en altitude. Cette dépendance s'exerce en ce sens que la cellule de précipitations est d'autant plus étendue que le vent augmente avec l'altitude.
    Notes: Zusammenfassung Die Untersuchung von Einzelfällen zeigt, daß die Größe der Horizontaldurchmesser von Schauerzellen offenbar stark von der vertikalen Windverteilung abhängt, und zwar in dem Sinne, daß die Niederschlagszellen um so größer sind, je stärker der Wind mit der Höhe zunimmt.
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    Meteorology and atmospheric physics 14 (1965), S. 427-440 
    ISSN: 1436-5065
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    Description / Table of Contents: Summary According toH. Dessens [1] the only factor that changes a thunderstorm into an intense hailstorm is a strong horizontal wind at heights between 6000 and 12000 m. The dependence of thunderstorm and hail on the direction and speed of upper wind on the southern slope of the Alps has been investigated by means of statistical methods. No significant correlation was found between these two values in this region. Of the factors which cause heavy hail during a thunderstorm the contribution of the speed of horizontal wind in altitudes amounts to less than 10%.
    Abstract: Résumé D'aprèsH. Dessens [1], le seul élément qui puisse déclencher de fortes chutes de grêle à partir d'un orage est un très fort vent horizontal entre 6000 et 12000 m d'altitude. Les auteurs examinent par des méthodes statistiques dans quelle mesure l'apparition d'orages et de grêle dépend, au sud des Alpes, de la force et de la direction du vent en altitude. Il en découle que, dans cette région, la relation entre le vent en altitude d'une part, les orages et la grêle d'autre part est peu marquée. Dans l'ensemble des facteurs qui provoquent la transformation d'un orage commun en un orage fortement grêligène, la vitesse du vent horizontal en altitude ne représente qu'un poids inférieur à 10%.
    Notes: Zusammenfassung Der einzige Faktor, der nachH. Dessens [1] Gewitter zu schweren Hagelgewittern werden läßt, ist ein sehr starker Horizontalwind in Höhen zwischen 6000 und 12000 m. Mit Hilfe statistischer Methoden wird untersucht, wie am Alpensüdfuß das Auftreten von Gewittern und Hagel vom Betrag und von der Richtung der Geschwindigkeit des Höhenwindes abhängt. Es stellt sich dabei heraus, daß hier der Zusammenhang zwischen diesen beiden Größen wenig ausgeprägt ist. Von der Gesamtheit der Faktoren, die bewirken, daß ein Gewitter zu einem schweren Hagelgewitter wird, beträgt der Anteil der Geschwindigkeit des horizontalen Höhenwindes weniger als 10%.
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    Meteorology and atmospheric physics 15 (1965), S. 26-31 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Summary The author derives the equations for a three-dimensional, nonaccelerated surface wind vector for the overflow over a mountain. He can show that it is not necessary to make the assumption of a stationary isentropic flow. By means of an approximation term the surface friction is also taken into consideration.
    Abstract: Résumé Dans ce mémoire, on établit un vecteur à trois dimensions dépourvu d'accélération; ce vecteur doit représenter un vent soufflant au sol par dessus une chaîne de montagnes. On démontre alors qu'il n'est pas nécessaire de faire intervenir l'hypothèse d'un courant isentrope stationnaire. On tient enfin compte du frottement au sol et cela par approximation.
    Notes: Zusammenfassung Es wird ein beschleunigungsfreier dreidimensionaler Windvektor an der Erdoberfläche bei Überströmung eines Gebirges abgeleitet. Dabei wird gezeigt, daß hierzu die Annahme einer stationären isentropen Strömung nicht notwendig ist. Weiters wird dann näherungsweise noch die Bodenreibung berücksichtigt.
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    Meteorology and atmospheric physics 15 (1965), S. 1-25 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Es wird der atmosphärische Ursprung der Ausfallprodukte, die einen plötzlichen Anstieg der Radioaktivität in Bodennähe verursachten, untersucht. Da alle Radioaktivitätsmessungen zeigten, daß das mittlere Alter der Ausfallprodukte in der Meßreihe größer als 100 Tage war, wird geschlossen, daß, im Hinblick auf eine angenommene mittlere Aufenthaltszeit der Ausfallprodukte in der Troposphäre von einem Monat, die Luft nicht lange vorher aus der Stratosphäre zugeströmt sein kann. Die Trajektorien der Schicht, die den plötzlichen Anstieg der Konzentration der Ausfallprodukte verursachte, wurden isentropisch vom Punkt des Anstiegs der Radioaktivität an zurückverfolgt. Die berechnete Trajektorie entspringt in der Region, die gewöhnlich als „Jet Stream Front” bezeichnet wird. Die Betrachtung der potentiellen Vorticity zeigt, daß die Luft eindeutig stratosphärischen Ursprungs war. Die absinkende Bewegung ist mit einer Zyklogenese in hohen Schichten in Verbindung, sie tritt an der Rückseite dieser Höhenzyklone auf. Bei Betrachtung auf einer Isobarenfläche scheint es, daß die Luft die Jetachse kreuzt; bei isentroper Betrachtung jedoch sieht man, daß die Trajektorie unter dem Jetkern „durchschlüpft” wobei keine größeren seitlichen Scherungen zu beobachten sind.
    Abstract: Résumé On recherche l'origine atmosphérique des résidus provoquant un accroissement brusque de la radioactivité au voisinage du sol. Comme toutes les mesures de la radioactivité ont montré que l'âge moyen des produits résiduels des différentes séries de mesure dépassait toujours 100 jours, on en conclut que, en admettant que ces particules se maintiennent en moyenne 1 mois dans la trophosphère, l'air ne parvient pas longtemps auparavant de la stratosphère. On a recherché la trajectoire inverse des masses d'air provoquant un accroissement subit de la retombée radioactive. Pour ce faire, on est parti du point où la dite recrudescence avait été constatée et, par des méthodes isentropiques, on a reconstitué la trajectoire présumée des produits résiduels. Les trajectoires ainsi calculées prennent naissance dans la région dénommée ordinairement „Jet Stream Front”. L'examen de la „vorticity” potentielle a montré que l'air a une origine stratosphérique indéniable. Le mouvement subsident est lié à une cyclogénèse à très haute altitude et se produit à l'arrière de la dite dépression. En considérant une surface isobarique, il semble que l'air traverse l'axe du courant. En considérant les choses de manière isentropique, on constate cependant que la trajectoire passe sous le noyau du courant de telle sorte qu'il n'y ait pas de cisaillement latérial appréciable.
    Notes: Abstract The atmospheric origin of the debris which produced a sudden increase of surface radioactivity is studied. Because all the radioactivity measurements show the mean debris ages to be greater than one hundred days for the entire sequence, the air is inferred to have been of recent stratospheric origin in view of an assumed mean tropospheric debris residence time of one month. The trajectories of the layer which caused the sudden increase in debris concentration were traced isentropically backward from the point of the fallout increase. The computed trajectory is seen to originate in the region traditionally considered to be the “jet stream front” and is shown definitely to be stratospheric air through potential vorticity considerations. The sinking motion is associated with upper air cyclogenesis and takes place to the rear of this high level cyclone. The air appears to cross the jet axis as viewed on an isobaric surface; but viewed isentropically, the trajectory is seen to “slip under” the jet core in such manner that no appreciable lateral shears are observed.
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    Meteorology and atmospheric physics 15 (1965), S. 118-128 
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    Meteorology and atmospheric physics 15 (1965), S. 129-167 
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    Description / Table of Contents: Zusammenfassung Die Theorie der Mondgezeiten in einer Atmosphäre mit zonalen Winden zeigt, daß der stärkste Einfluß vonvertikalen Windänderungen in mittleren Breiten herrührt. Wenn das zonale Windsystem aber genau antisymmetrisch zum Äquator ist, hat es keinen Einfluß; nur der Teil mit äquatorieller Symmetrie wirkt auf die Gezeiten. Es besteht die Möglichkeit, daß die beobachtete jahreszeitliche Schwankung der Mondgezeit durch jahres-zeitliche Schwankungen des zonalen Windsystems erklärt werden kann; aber für den Beweis würde man mehr Information über die zonalen Winde in der Südhemisphere brauchen, als bis jetzt vorhanden ist. Eine andere mögliche Erklärung der jahreszeitlichen Änderung der Mondgezeit, nämlich als eine Folge jahreszeitlicher Schwankungen der mittleren vertikalen Temperatur-verteilung für die ganze Erde, muß noch untersucht und mit den vorliegenden Resultaten verglichen werden.
    Abstract: Résumé La théorie des marées lunaires agissant sur une atmosphère ne présentant que des vents zonaux montre que la plus forte influence modificatrice se produit par des variations verticales du vent dans les latitudes moyennes. Cependant, lorsque le système des vents zonaux est exactement antisymétrique par rapport à l'équateur, il n'y a pas d'influence. Seules les parties symétriques à l'équateur ont une influence sur les marées lunaires. Il est possible que les variations saisonnières de la marée lunaire observées puissent être expliquées par des variations également saisonnières du système des vents zonaux. Pourtant, pour le prouver, on devrait disposer de plus d'informations que jusqu'ici sur les vents zonaux de l'hémisphère sud. Une autre explication possible des variations saisonnières des marées lunaires serait celle d'une conséquence des variations saisonnières de la répartition verticale de la température moyenne pour la terre entière. Cette hypothèse doit encore être étudiée et comparée aux résultats de la présente étude.
    Notes: Summary Lunar tidal oscillations of an atmosphere with zonal winds are discussed theoretically. The main effect comes from vertical wind shears of middle latitude zonal winds. If, however, the zonal wind system is strictly antisymmetric with respect to the equator, there is no effect of the wind system. It is the equator-symmetric component of zonal wind systems that plays an important role. The meridional temperature gradient has no pronounced influence. There is a possibility that the observed annual variations of the lunar tide can be interpreted as a result of seasonal variations of zonal wind systems. But the proof requires information about the zonal winds in the southern hemisphere which is not yet available. Another possibility, namely the interpretation of the seasonal variation as a result of annual variations of global mean vertical temperature profile remains to be investigated and compared to the present result.
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    Meteorology and atmospheric physics 15 (1965), S. 205-226 
    ISSN: 1436-5065
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    Topics: Geography , Physics
    Description / Table of Contents: Summary The relation between the lunar phase and the occurrence of precipitation ≧10,0 mm per day per station in northern Germany is presented. The revealed connection is also significant if local and temporal auto-correlations caused by the nature of atmospheric processes are accounted for. Morphologically, the derived picture is well matching the results in other parts of the world. This suggests world-wide relationships, which are briefly discussed.
    Abstract: Résumé On montre ici la relation entre les phases de la lune et les chutes de pluie dépassant 10,0 mm par jour et pour station dans la région du nord de l'Allemagne. Ce rapport se situe au-dessus de la répartition normale, même si l'on tient compte des auto-corrélations dans le temps et dans l'espace, répercussions dues aux conditions météorologiques L'image ainsi obtenue s'apparente morphologiquement à des phénomènes observés ailleurs et laisse entrevoir des relations à l'échelle mondiale. Ces relations sont en outre brièvement discutées.
    Notes: Zusammenfassung Es wird der Zusammenhang zwischen der Mondphase und dem Ereignis eines Niederschlages ≧10,0 mm pro Tag und Station für Norddeutschland dargestellt. Der Zusammenhang ist auch bei Berücksichtigung der wetterbedingten örtlichen und zeitlichen Autokorrelation überzufällig. Morphologisch ordnet sich das gewonnene Bild in Ergebnisse aus anderen Erdteilen ein und deutet weltweite Zusammenhänge an, die kurz diskutiert werden.
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    Meteorology and atmospheric physics 15 (1965), S. 192-204 
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    Description / Table of Contents: Summary After a short discussion of the theoretical background for the calculation of the spreading of the noxious pollutants of the air based on the laws of turbulent diffusion a formula is derived for the concentration of the immisison on the ground with help of the empirical relations between the dispersion measures and the distance from the source given byPasquill. In some examples the concentration field at the ground relative to the point of maximum immission is calculated, considering a fixed height of the funnel of 40 m and a quantity of noxious gases as usually found with average emittents. The figures show a strong modification of the concentration field by the meteorological situation according to whether the spreading type is stable, indifferent or unstable.
    Abstract: Résumé On discute tout d'abord brièvement les fondements théoriques permettant de calculer la propagation des pollutions atmosphériques; pour ce faire, on se base sur les lois de la diffusion turbulente. On en tire ensuite une formule de calcul de la concentration des immissions à l'aide des relations empiriques dePasquill, relations existant entre les quantités répandues et la distance de la source. On calcule au moyen d'une série d'exemples le champ des concentrations au sol par rapport au point de concentration maximum; pour ce faire, on admet und chemineé fixe de 40 mètres de hauteur et une quantité de gaz nocifs correspondant à une moyenne de polluants. Les figures montrent la forte modification que subit la répartition des concentrations selon les conditions météorologiques, en d'autres termes si l'on a affaire à un type de propagation stable, indifférent ou instable.
    Notes: Zusammenfassung Nach einer kurzen Diskussion der theoretischen Grundlagen für die Berechnung der Ausbreitung von schädlichen Beimengungen der Luft auf Grund der Gesetzmäßigkeiten der turbulenten Diffusion wird mit Hilfe der vonPasquill angegebenen empirischen Beziehungen zwischen Streuungsmaßen und Quelldistanz die Formel für die Immissionskonzentration am Boden abgeleitet. An Hand einer Reihe von Beispielen wird das Bodenkonzentrationsfeld relativ zu dem Punkt maximaler Immissionskonzentration berechnet, wobei eine feste Schornsteinhöhe von 40 m und eine für mittlere Emittenten zutreffende Auswurfmenge an schädlichen Gasen vorausgesetzt wird. Die Abbildungen zeigen die starke Modifikation des Konzentrationsfeldes durch die meteorologischen Verhältnisse, je nachdem, ob ein stabiler, indifferenter oder labiler Ausbreitungstyp vorliegt.
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    Monatshefte für Mathematik 69 (1965), S. 1-17 
    ISSN: 1436-5081
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    Monatshefte für Mathematik 69 (1965), S. 58-61 
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    Monatshefte für Mathematik 69 (1965), S. 30-34 
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    Monatshefte für Mathematik 69 (1965), S. 62-68 
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    Monatshefte für Mathematik 69 (1965), S. 104-104 
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    Monatshefte für Mathematik 69 (1965), S. 146-150 
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