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  • 1
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    Bulletin of mathematical biology 30 (1968), S. 1-1 
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  • 2
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    Bulletin of mathematical biology 30 (1968), S. 27-32 
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    Notes: Abstract In a previous paper (Bull. Math. Biophysics,29, 565–574, 1967) the author developed equations to represent velocity and hematocrit profiles in quasi-Poiseuille flow of blood. It was assumed that energy dissipation was minimized and that the viscosity depended on hematocrit and shear rate according to the Casson formula. These equations are simplified considerably, placed in a form more suitable for numerical solution and shown to depend on a single dimensionless parameter. Typicalin vivo values for this parameter are calculated.
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  • 3
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    Bulletin of mathematical biology 30 (1968), S. 33-46 
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    Notes: Abstract In this paper, discrete models of reproduction are studied. In part one, definitions are given, particularly on order of the reproduction; part two concerns the growth of the population; part three, the phenomena of delay or acceleration; and part four, the consequences of mortality.
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    Bulletin of mathematical biology 30 (1968), S. 3-26 
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    Notes: Abstract A model of the regulation of thyroid hormone in the bloodstream of living systems is formulated and analyzed. The portion of this model defined as theregulator includes components representing the thyroid, anterior pituitary and hypothalamic organs and their intercommunicating channels, that is, the peripheral plasma and hypophysial portal circulations and certain neuro-secretory connections. The loss of hormones from the plasma in the living system associated with physiological mechanisms within the peripheral tissue space and the excretory pathways is represented in the model by a lumpedload on the regulator. The model is reduced to a system of differential equations involving eleven parameters and variables, all of which are identified with certain physiological structures and states. Five of these are currently observable by available laboratory techniques and two others are computable explicity from the equations of the model; the remaining four can be computed in the same way to within a multiplicative constant. Procedires for carrying out ten of these measurements and calculations are suggested. On the basis of the equations and parameters of the model, a discussion of the normal behavior and the response of this system to certain types of disturbances is presented. A systematic effort has been made in the development of this model to include all relevant physiological data and relationships reported in the biological literature. A summary of this literature, reflecting the views and interpretations made by the authors of this paper, is included for completeness and ease of reference.
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    Bulletin of mathematical biology 30 (1968), S. 47-59 
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    Notes: Abstract In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.
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    Bulletin of mathematical biology 30 (1968), S. 87-104 
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    Notes: Abstract A method for the identification of flow systems by frequency domain analysis has been extended to include systems with recirculation and truncated data curves. Application of the technique to clinical indicator-dilution curves indicates that the method may be useful in the quantitation of intracardiac shunts. A number of numerical examples which demonstrate the accuracy of the method are included.
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    Bulletin of mathematical biology 30 (1968), S. 61-86 
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    Notes: Abstract By assigning time-varying coordinates to all environmental stimuli, it has been possible to axiomatize psychoanalytic theory on the five principles of multiple causation, growth-aging influence, genetic influence, historic influence and conscious-unconscious activity. The theorems of summation of response and the inevitability of conscious-unconscious conflict with their corollaries follow directly from the axiomatic foundations, as does the existence of an adaptation-defense mechanism. The interpretation of the defense mechanism in terms of an ego-id feedback system provides the basis for the structural existence of conscious-conscious and unconscious-unconscious conflict.
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    Bulletin of mathematical biology 30 (1968), S. 117-122 
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    Notes: Abstract In previous studies of (M,R) (Rosen, 1961; Demetrius, 1966), it was assumed that changes in the structure of (M,R) which were induced by environmental alternations occurred without error. Here, the effect of both “genetic” and “metabolic” malfunctions on the behavior of (M,R) is examined and a subclass of these systems whose behavior is invulnerable to such errors is specified.
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    Bulletin of mathematical biology 30 (1968), S. 105-116 
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    Notes: Abstract The definition of an (M,R) is formulated in a way that emphasizes its mathematical properties. Neglecting interactions between the components, it is shown that: (1) An (M,R) contains only one non-reestablishable component. (2) If an (M,R) contains only one non-reestablishable component, then that component is central. Examples are given to illustrate the biological significance of these two results. The notion of “lag-independence” is introduced, and it is shown that if a system possesses only one non-reestablishable component which is “lag-independent” then all components are lag-independent. The concepts of reestablishability, centrality and lag-independence are applied in order to suggest various criteria for optimal organization of (M,R).
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    Bulletin of mathematical biology 30 (1968), S. 123-133 
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    Notes: Abstract A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ f of a mappingf: A→B in the stimulated Φ1 and unstimulated state Φ0. Likewise, the range of τ is formed by the set δ={f o ,f 1} wheref 1 means the mappingf in its stimulated state andf o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.
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    Bulletin of mathematical biology 30 (1968), S. 135-151 
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    Notes: Abstract The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.
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    Bulletin of mathematical biology 30 (1968), S. 153-162 
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    Notes: Abstract In a previous paper (Bull. Math. Biophysics,22, 257–262, 1960), an expression for the probability that a car jumps off a road as a function of the speed and the size of the car was derived mostly from geometric and kinematic considerations, introducing only the reaction time as a biological parameter. In subsequent papers (Bull. Math. Biophysics,29, 181–186, 187–188, 1967) a more detailed study was made of the exact shape of the tracking curve of the car which involved several biological parameters of the driver. In the present paper the results of the previous studies are combined, and a more general equation for the probability of jumping off the road is obtained. This probability, as in the earlier study, increases with the speedv, widths o and lengthl o of the car, and decreases with widths of the lane. However, this probability also depends on several parameters which characterize the psychobiological constitution of the driver. Unpublished experiments by Ehrlich, which corroborate the general conclusions, are briefly described.
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    Bulletin of mathematical biology 30 (1968), S. 205-213 
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    Bulletin of mathematical biology 30 (1968), S. 163-174 
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    Notes: Abstract The theory of organismic sets, developed in previous papers (Bull. Math. Biophysics,29, 139–152; 389–393; 643–647) is further generalized. To conform better with some biological and sociological facts the basic definitions are made more general. The conclusion is reached that every organismic setS o is in general the union of three disjoined subsetsS o1 ,S o2 andS o3 . Of these the subsetS o1 , called the “core” is equivalent to an organismic set defined in previous publications. Its functioning is essential for the functioning ofS o . The subsetsS o2 andS o3 , taken alone, are not organismic sets. The first of them is responsible for such biological or sociological functions which are not necessary for the “immediate” survival ofS o but which are important for adaptation to changing environment and are therefore essential for a “long range survival.” The second one,S o3 , is responsible for biological or social functions which are irrelevant for the survival ofS o . Biological and sociological examples ofS o2 andS o3 are given. In addition to the fundamental theorem established in the first of the above mentioned papers, three new conclusions are derived. One is that in organismic sets of order higher than zero not all elements are specialized. The second is that every organismic set of order higher than zero is mortal. The third is that with increasing specialization the intensities of some activities in some elements ofS o are reduced. Again the biological and sociological examples are given. At the end some very general speculations are made on the possible relation between biology and physics and on the possibility of “relationalizing” physics.
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    Bulletin of mathematical biology 30 (1968), S. 175-204 
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    Notes: Abstract The structural information content (Rashevsky, 1955; Trucco 1956a, b)I g (X) of a graphX is defined as the entropy of the finite probability scheme constructed from the orbits of its automorphism groupG(X). The behavior ofI g on various graph operations—complement, sum, join, cartesian product and composition, is examined. The principal result of the paper is the characterization of a class of graph product operations on whichI g is semi-additive. That is to say, conditions are found for binary operations o and ∇ defined on graphs and groups, respectively, which are sufficient to insure thatI g (X o Y)=I g (X)+I g (Y)−H XY , whereH XY is a certain conditional entropy defined relative to the orbits ofG(X o Y) andG(X) ∇G(Y).
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    Bulletin of mathematical biology 30 (1968), S. 215-224 
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    Notes: Abstract The mathematical treatment of three models of possible development of a society with a dominance relationship is discussed. The conclusion is reached that social factors as well as inherent characteristics need to be introduced to account for near-hierarchical structures. This is not a surprising conclusion; however, deriving it from mathematical considerations should be of interest to the mathematical sociologist since it puts the problem into theoretical perspective. Also these considerations may suggest quantitative observations or experimental tests and given indications as to their analysis.
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    Bulletin of mathematical biology 30 (1968), S. 291-298 
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    Notes: Abstract Some of the properties of the equations describing three species living in competition in the same environment are analysed. In particular it is found that, under certain conditions, the size of the three populations can oscillate.
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    Bulletin of mathematical biology 30 (1968), S. 299-308 
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    Notes: Abstract Expressions are obtained for the pulse velocities in cylindrical tubes of rubber-like materials which are under a state of initial stress. The development is based on the theory of finite elastic deformations and a Mooney materials is considered for illustrative purposes. Numerical results are given in terms of dimensionless parameters which involve the stretch ratio and lumen volume ratio. For the thoracic aorta, a value for the pulse velocity is obtained which is lower than the experimental value.
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    Bulletin of mathematical biology 30 (1968), S. 309-318 
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    Notes: Abstract A macroscopic conservation equation is derived for electromagnetophoresis of a dilute suspension. The governing equation and auxiliary conditions are formulated for transport in a rectangular cell, these being reduced to standard form by dimensional methods.
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    Bulletin of mathematical biology 30 (1968), S. 319-323 
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    Notes: Abstract The relationships between various size distributions in balanced exponential growth of a batch culture of microorganisms are presented. Starting from the partial differential integral equations (Eakmanet al., 1966; Fredricksonet al., 1967) derived for the growth of a microbial culture expressions are obtained for the growth rate of organisms of specific size and size range. These expressions were first obtained by Collins and Richmond (1962) by an entirely different method. Also derived are equations which link probability functions, which are basic to the growth of a microbial culture, with other size distributions that can be estimated experimentally.
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    Bulletin of mathematical biology 30 (1968), S. 325-331 
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    Notes: Abstract Under the assumption of simple Fick-law diffusion with convection and/or imposed force fields, the flux law for tagged molecules in a tracer system is derived, and the Sheppard-Householder interfusion coefficient identified. The partial differential equations for concentrations of tagged species and for specific activities in an open distributed reaction system are derived and compared.
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    Bulletin of mathematical biology 30 (1968), S. 333-340 
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    Notes: Abstract Two theorems relating to properties of the solutions of the equations of continuity for the concentrations of the chemical species in a diffusion-reaction system are proved. The theorems concern boundary conditions under which the flux of a specified species can be guaranteed to be directed into the reaction region and the circumstances under which any two of the conditions (i) stationarity, (ii) flux equilibrium, and (iii) chemical equilibrium, imply the third. Application of these theorems to apparent active transport and to the properties of the differential equations for specific activities in a distributed tracer system are noted.
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    Bulletin of mathematical biology 30 (1968), S. 341-349 
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    Notes: Abstract Recent experiments on so-called chemical transfer of memory may indicate at first glance that the possibility of transfer of the memory of a large number of reaction patterns in this manner requires the assumption of a correspondingly large number of specific chemical substances. It is shown that this is not necessarily the case. A mechanism is conceivable in which a single substance is responsible for “memory” transfer for a large number of distinct patterns. Mechanisms involving only about one hundred different specific substances could conceivably be responsible for chemical transfer of memory of some 1050 spatial patterns.
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    Bulletin of mathematical biology 30 (1968), S. 351-353 
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    Notes: Abstract It is suggested how nonoriented graphs may be used to representn-ary relations in organisms and to study the changes in variousn-ary relations under the transformation proposed in a previous paper (Bull. Math. Biophysics,16, 317–348, 1954).
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    Bulletin of mathematical biology 30 (1968), S. 355-357 
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    Notes: Abstract It is suggested that the development of organismic sets is governed not by the maximalization of the integral survival value, as suggested previously (Bull. Math. Biophysics,28, 283–308, 1966;29, 139–152, 1967;30, 163–174, 1968), but by maximizing the number of new relations which appear as an organismic set develops.
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    Bulletin of mathematical biology 30 (1968), S. 387-414 
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    Notes: Abstract The connection between the adjacency matrix and the automorphisms of a digraph is used to develop a method for studying the automorphism group and, thus, the information content (Mowshowitz 1968a, b) of a digraph. An algorithm is given for constructing digraphs with zero information content, and the properties of such digraphs are examined. Moreover, an algorithm for computing the automorphism group of a digraph is presented and is used to find conditions which insure that two digraphs have the same information content. This algorithm is further used to determine the information content of digraphs whose adjacency matrices have prescribed properties.
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    Bulletin of mathematical biology 30 (1968), S. 359-385 
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    Notes: Abstract The arterial system is characterized geometrically as a system of branched elastic fluid lines whose frequency response is then known in the sense of the Fourier transform. For convenience of visualization the transient response of the individual tube to an input pressure-flow pair is represented in the time domain by kernel functions indicating the hybrid effect of viscosity and momentum on the line impedance and damping characteristics. The system as a whole is then divided into a zone of smaller tubes (below 3 mm) and a zone of larger tubes extending up to the aorta. It is shown that as a system each labyrinth of tubes below the 3 mm size may be replaced by a single impedance transformation which is dominantly resistive-capacitive. In the larger tubes, the transformation of the pulse wave at different stations is considered a point of interest. Therefore hand calculated examples are worked to derive the response of a system involving some of the larger vessels to a pressure or flow pulse of the typical shape seen near the heart. The result suggests that the dicrotic wave seen in the pressure pulse of mammals is due to the hybrid viscosity-momentum nature of the longer fluid lines in relation to the gradation of unmatched terminal impedances with which they are terminated. Damping of the higher frequency components is also accounted for.
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    Bulletin of mathematical biology 30 (1968), S. 427-435 
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    Notes: Abstract Generalized equations are developed for the age structure of growing cell populations when other parameters besides chronological age are taken into account. These are summarized in a parameter which we call “chronological age”. The theory is Markovian in spirit and leads to an integro-differential equation for population density which generalizes several equations now appearing in the literature. Approximations to the fundamental equation are suggested.
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    Bulletin of mathematical biology 30 (1968), S. 415-425 
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    Notes: Abstract A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete self-reproduction and complete self-explanation. These latter concepts are shown to be independent from ordinary logical-mathematical-biological reasoning, and a special form of complete self-reproduction is shown to be axiomatizable. Involved is the question whether there exists a function that belongs to its own domain or range. Previously, Wittgenstein has argued, on intuitive grounds, that no function can be its own argument. Similarly, Rosen has argued that a paradox is implied by the notion of a function which is a member of its own range. Our result shows that such functions indeed are independent from ordinary logical-mathematical reasoning, but that they need not imply any inconsistencies. Instead such functions can be axiomatized, and in this sense they really do exist. Finally, the introduced notion of complete self-reproduction is compared with “self-reproduction” of ordinary biological language. It is pointed out that complete self-reproduction is primarily of interest in connection with formal theories of evolution.
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    Bulletin of mathematical biology 30 (1968), S. 437-453 
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    Notes: Abstract A theoretical model of the cornea based on corneal dimensions and reported properties is presented in this paper. It is shown that because of large differences in the thicknesses of the Bowman’s and Descemet’s membranes and the stroma, and because of the reported large differences in the elastic properties of the layers, a sandwich-shell model is a good approximation for the study of corneal deformation. The theory is applicable for applanation tonometry. A set of equilibrium equations based on Reissner’s theory is given. Shell parameters which determine the behavior of shells are expressed in terms of the corneal properties and dimensions. Numerical examples which show the effects of corneal parameters on the stress resultants due to intraocular pressure are also given.
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    Bulletin of mathematical biology 30 (1968), S. 553-563 
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    Notes: Abstract A study was made of populations in stationary equilibrium that satisfy the following conditions: (1) The birth rate is very large in relation to the capacity of the habitat. (2) The part of the mortality which is independent of age is easily measured and is found to be very high. For these populations the following conclusions were drawn from the experimental observations: (1) The populations in steady state show an inversely proportional relation between the maximum average age of its components and the mortality. (2) The biomass of a population in a steady state saturating a habitat remains constant in spite of changes in the mortality. (3) The population of organisms continually growing through life, whose steady-state equilibria are reached under conditions of high mortality are composed of great numbers of individuals with a small average size. The equilibria which are reached under conditions of low mortality are characterized by a small number of individuals with large average size.
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    Bulletin of mathematical biology 30 (1968), S. 565-579 
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    Notes: Abstract A mathematical model for learning of a conditioned avoidance behavior is presented. An identification of the net excitation of a neural model (Rashevsky, N., 1960.Mathematical Biophysics. Vol. II. New York: Dover Publications, Inc.) with the instantaneous probability of response is introduced and its usefulness in discussing block-trial learning performances in the conditioned avoidance situation is outlined for normal and brain-operated animals, using experimental data collected by the author. Later, the model is applied to consecutive trial learning and connection is made with the approach of H. D. Landahl (1964. “An Avoidance Learning Situation. A Neural Net Model.”Bull. Math. Biophysics,26, 83–89; and 1965, “A Neural Net Model for Escape Learning.”Bull. Math. Biophysics,27, Special Edition, 317–328) wherein lie further data with which the model can be compared.
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    Bulletin of mathematical biology 30 (1968), S. 581-614 
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    Bulletin of mathematical biology 30 (1968), S. 455-479 
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    Notes: Abstract The author’s theory of speech perception, as applied to time-dependent speech sounds, leads to many testable predictions. While some of these predictions are consistent with conventional knowledge, others are new and quite unexpected. A few are in contradiction to long accepted experimental results. A computer-aided experimental program, designed to test the theory, wholly supported these predictions. In view of this outcome, it seems desirable to test other predictions of the theory and to reexamine some conventionally accepted views in order to arrive at a more comprehensive theory of speech. The present findings indicate that, apart from categorization, consonants are similar to vowels: they exhibit parallel organizations and transformation properties.
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    Bulletin of mathematical biology 30 (1968), S. 519-525 
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    Notes: Abstract In our recent book,Looking at History Through Mathematics (MIT Press, 1968), we discussed two possible mechanisms of a transition of a society from an “arational” behavior, in which most things are accepted uncritically on faith, to a rational behavior, characterized by a critical appraisal of everything. Both mechanisms lead to irreversible changes, which eventually result asymptotically in a complete rationalization of society. In the present paper it is shown that a generalization of the second mechanism may lead to alternations between rational and arational behavior of a society. The reversal from rational to arational behavior is due to the circumstance that for some people hard thinking is either impossible or at least highly unpleasant. It appears, on the basis of the model discussed here, that acomplete rationalization of any society is unattainable.
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    Bulletin of mathematical biology 30 (1968), S. 529-529 
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    Bulletin of mathematical biology 30 (1968), S. 751-760 
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    Notes: Abstract Previous studies of L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956) of possible biochemical periodicities in organisms assumed non-linear biochemical interaction between different metabolites, because linear systems do not lead to undamped ocsillations. They treated homogeneous systems. Later N. Rashevsky generalized their results to a more realistic case where the non-homogeneity due to the histological structure is considered. (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1964;Bull. Math. Biophysics,29, 389–393, 1967.) As long as the histological structure remains constant, the existence of sustained periodicities requires the assumption of non-linearity of biochemical interactions. If, however, the secretions of an endocrine gland affect the histological structure of the target organ, notably as in the menstrual cycle, and if there is a feed-back, the equations become non-linear and may admit sustained periodic solutions even if the purely biochemical interactions are linear.
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    Monatshefte für Mathematik 72 (1968), S. 1-5 
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    Monatshefte für Mathematik 72 (1968), S. 6-8 
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    Monatshefte für Mathematik 72 (1968), S. 9-17 
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    Monatshefte für Mathematik 72 (1968), S. 38-44 
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    Monatshefte für Mathematik 72 (1968), S. 61-71 
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    Monatshefte für Mathematik 72 (1968), S. 72-96 
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    Monatshefte für Mathematik 72 (1968), S. 107-117 
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    Monatshefte für Mathematik 72 (1968), S. 118-132 
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    Monatshefte für Mathematik 72 (1968), S. 97-106 
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    Monatshefte für Mathematik 72 (1968), S. 137-143 
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    Monatshefte für Mathematik 72 (1968), S. 133-136 
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    Monatshefte für Mathematik 72 (1968), S. 152-156 
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    Monatshefte für Mathematik 72 (1968), S. 144-146 
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    Monatshefte für Mathematik 72 (1968), S. 168-192 
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    Monatshefte für Mathematik 72 (1968), S. 147-151 
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    Monatshefte für Mathematik 72 (1968), S. 157-167 
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    Monatshefte für Mathematik 72 (1968), S. 200-211 
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    Monatshefte für Mathematik 72 (1968), S. 220-223 
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    Monatshefte für Mathematik 72 (1968), S. 193-199 
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    Monatshefte für Mathematik 72 (1968), S. 212-216 
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    Monatshefte für Mathematik 72 (1968), S. 224-238 
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    Monatshefte für Mathematik 72 (1968), S. 217-219 
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    Monatshefte für Mathematik 72 (1968), S. 254-263 
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    Monatshefte für Mathematik 72 (1968), S. 239-244 
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    Monatshefte für Mathematik 72 (1968), S. 270-288 
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    Monatshefte für Mathematik 72 (1968), S. 245-253 
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    Monatshefte für Mathematik 72 (1968), S. 264-269 
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    Monatshefte für Mathematik 72 (1968), S. 296-302 
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    Monatshefte für Mathematik 72 (1968), S. 325-334 
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    Monatshefte für Mathematik 72 (1968), S. 289-295 
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    Monatshefte für Mathematik 72 (1968), S. 335-346 
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    Monatshefte für Mathematik 72 (1968), S. 315-324 
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    Monatshefte für Mathematik 72 (1968), S. 303-314 
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    Monatshefte für Mathematik 72 (1968), S. 355-367 
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    Monatshefte für Mathematik 72 (1968), S. 347-354 
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    Monatshefte für Mathematik 72 (1968), S. 368-381 
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    Monatshefte für Mathematik 72 (1968), S. 382-384 
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    Monatshefte für Mathematik 72 (1968), S. 385-411 
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    Monatshefte für Mathematik 72 (1968), S. 412-418 
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    Monatshefte für Mathematik 72 (1968), S. 419-426 
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    Monatshefte für Mathematik 72 (1968), S. 427-430 
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    Monatshefte für Mathematik 72 (1968), S. 431-431 
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    Monatshefte für Mathematik 72 (1968), S. 432-444 
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    Monatshefte für Mathematik 72 (1968), S. 445-450 
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    Monatshefte für Mathematik 72 (1968), S. 451-463 
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    Colloid & polymer science 222 (1968), S. 62-63 
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    Colloid & polymer science 222 (1968), S. 77-78 
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    Colloid & polymer science 222 (1968), S. 86-91 
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    Colloid & polymer science 222 (1968), S. 95-96 
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    Colloid & polymer science 222 (1968), S. 103-110 
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    Description / Table of Contents: Summary α-keratose isolated from wool was fractionated by gelchromatography under optimum conditions — using Sephadex G 75 in 5 m columns and mild alkaline-buffered solutions of theα-keratose. Theα-keratose was separated into three main parts: a very heterogeneous component calledα KA protein, a very small fraction namedα KB1-protein and a pure proteinα 2KB (6% of total wool). After rechromatography of theα KB2-fraction the molecular weight of the protein was estimated to be 8300. Analysis of the N-terminal endgroups showed that theα KB2-protein contains the same N-terminal amino acids as wool; but there is only one C-terminal amino acid (tyrosine). A very high content of tyrosine, phenylalanine and glycine was found by amino acid analysis of theα KB2-protein.
    Notes: Zusammenfassung Aus Merino-Kammzug isolierteα-Keratose wurde mit Hilfe verschiedener Sephadex-Gele chromatographisch aufgetrennt. Die besten Trenneffekte konnten dabei mit Sephadex G 75 in 5 m langen Säulen unter Verwendung von schwach alkalischen Puffern erzielt werden; neben einer sehr heterogenen Hauptkomponenteα KA und einer in sehr geringer Konzentration vorhandenen Fraktionα KB1 wurde ein in Wolle zu 6% vorhandenes einheitliches Proteinα KB2 isoliert. Nach Rechromatographie der Fraktionα KB2 wurde deren Molekulargewicht mit Hilfe der Ultrazentrifuge zu 8300 bestimmt. Dasα KB2-Protein wies alle auch in Wolle vorhandenen sieben N-terminalen Endgruppen, aber nur Tyrosin als C-terminale Endgruppe auf. Aminosäureanalysen zeigten einen hohen Gehalt der Aminosäuren Tyrosin, Phenylalanin und Glycin an.
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    Colloid & polymer science 222 (1968), S. 124-130 
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    Description / Table of Contents: Zusammenfassung Die freie Oberflächenenergie von Polyäthylenkristallen wurde aus der Auflösungstemperatur der Kristalle in dem Lösungsmittel, aus dem sie gebildet wurden, über thermodynamische Betrachtungen abgeschätzt. Aus der Größe der freien Oberflächenenergie und der Dichte der Einkristalle wurde die in der vorhergehenden Veröffentlichung angegebene Folgerung bestätigt, daß die Oberfläche um so regelmäßiger ausgebildet wird, je größer der thermodynamische Wechselwirkungsparameter und das Molvolumen des Lösungsmittels sind.
    Notes: Summary To investigate the effect of solvent on polyethylene single crystal formation, the end surface free energy of lamellae was estimated from the dissolution temperature of single crystal in solvent from which single crystals were formed, by the equation based on the thermodynamic consideration. The density measurements of the single crystal were also carried out in a density gradient column, further to obtain informations about solvent effect on single crystal formation. From the results on the end surface free energy and the density of single crystals, the conclusion obtained in the preceding paper, that more regular surface may be formed with solvent having larger thermodynamic interaction parameter and larger molar volume, was confirmed.
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    Colloid & polymer science 222 (1968), S. 56-61 
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    Description / Table of Contents: Zusammenfassung Zur Bestimmung der Oberflächen-OH-Gruppen im Knochenmineral, welches als unreiner Hydroxyl-apatit beschrieben werden kann, wurde Lithium-Aluminiumhydrid in Diglymelösung verwendet. Die Menge der OH-Gruppen wurde aus der entwickelten Wasserstoffmenge berechnet. Ein Vergleich der auf diesem Wege ermittelten Menge an OH-Gruppen mit der aus der spezifischen Oberfläche (BET N2-Adsorption) und der Kristallstruktur errechneten zeigt ein Defizit von mehr als 50%. Zur Deutung werden mehrere Möglichkeiten diskutiert. Die Annahme, daß echte Fehlstellen für die Oberflächen-OH-Gruppen vorliegen, wird bevorzugt.
    Notes: Summary Lithium aluminium hydride reagent has been employed in the determination of surface OH groups in bone mineral which may be described as an impure hydroxyapatite. The dehydrated sample is dropped into a diglyme solution of LiAlH4 and hydrogen gas evolution is measured. One mole of hydrogen is evolved by each mole of OH groups. The total surface is previously measured by the B.E.T. nitrogen adsorption method. Thus it is possible to compare the number of surface OH groups found per unit area with that estimated on the basis of the known crystal lattice. Less than fifty percent of the estimated number is found. Several possible explanations for the apparent discrepancy are offered. Perhaps the most compelling one is the suggestion of an actual deficiency of surface hydroxyl groups.
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    Colloid & polymer science 222 (1968), S. 187-188 
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    Colloid & polymer science 222 (1968), S. 191-192 
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    Colloid & polymer science 223 (1968), S. 13-23 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Zusammenfassung Die komplexe Dielektrizitätskonstante von trockenem Rhinozeros Horn wurde über ein Frequenzintervall von 10−6 bis 10+6 Hz und ein Temperaturintervall von −14 °C bis 125 °C gemessen. Trockene Wolle wurde ebenfalls geprüft, aber nur für ein Frequenzintervall von 10−2 bis 106 Hz. Die Resultate lassen sich auf Grund der 6 gefundenen Absorptionsgebiete, ihres Verhaltens und der Aktivierungsenergien erklären. Der Vergleich mit den mechanischen und dielektrischen Eigenschaften der Polyamide wurde angestellt.
    Notes: Summary The complex dielectric constant of dry rhinoceros horn has been measured over the frequency range of 10−6 c′s to 106 c′s and the temperature range −14 °C to 125 °C. Dry wool has been similarly tested but for a frequency range of 10−2 c′s to 106 c′s. The results have been analysed into six absorption regions and the properties of these absorptions, including their activation energies, have been derived and discussed. A comparison has been made with the mechanical and dielectric properties of the polyamides.
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  • 97
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    Colloid & polymer science 223 (1968), S. 6-13 
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary A description is given of the measurement of the velocity of dissolution with the help of an interference microscope. A swollen surface layer of constant thickness determines the rate of this stationary process. The mutual (D) and the intrinsic diffusion coefficient of the solvent (dlm) can be determined throughout the whole range of concentrations.D shows a maximum and DLM a monotonous increase with the volume fraction of the solvent. The influence of the size of the solvent molecule is investigated with the help of a series of esters with increasing paraffin sceleton. The interdependence of thermodynamic and kinetic quality of a solvent on the swollen surface layer is shown schematically. The poorest solvent methylacetate exhibits a new type of dissolution: The surface layer with partial miscibility. It is described in detail.
    Notes: Zusammenfassung Es wird eine Anordnung beschrieben, die es mit Hilfe eines Interferenzmikroskopes gestattet, das Verhalten eines Polymeren in einem strömenden Lösungsmittelfeld genau zu studieren. Bei der Auflösung im stationären Zustand bildet sich auf der Polymeroberfläche eine Diffusionsgrenzschicht, die die Geschwindigkeit des gesamten Prozesses steuert. Aus dem Konzentrationsverlauf in dieser Schicht und der Auflösungsgeschwindigkeit lassen sich der differentielle gemeinsame DiffusionskoeffizientD und der Eigendiffusionskoeffizient des Lösungsmittels DLM über den gesamten Konzentrationsbereich bestimmen.D durchläuft ein Maximum, wähernd DLM mit dem Volumenbruch des Lösungsmittels stetig steigt. Untersuchungen an Polystyrol (M=63000) mit einer Esterreihe (Äthyl-Amyl-acetat) geben interessante Aufschlüsse über die Wirkung der Lösungsmittelmolekülgröße auf den stationär verlaufenden Diffusionsprozeß, So zeigt sich das thermodynamisch nicht besonders gute Lösungsmittel Äthylacetat gegenüber den anderen Estern als kinetisch sehr wirkungsvoll. Auch findet man einen Lösungsmitteleinfluß bei der Hemmung der Diffusion in einem Konzentrationsbereich, in der Verschlingung der Makromoleküle die Beweglichkeit stark verringern. Einen neuen Auflösungstyp lernen wir beim Methylacetat kennen. Es ist die Auflösung mit Entmischung in der Gelphase.
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  • 98
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    Colloid & polymer science 223 (1968), S. 24-30 
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Summary From the theories of light scattering of colloidal spheres (Mie, Zimm andDandliker) a method was derived, which allows the determination of the diameter and the refractive index of spherical particles by measuring specific turbidity and refractive index increment. The method requires only small experimental equipment and is simple in measurement and evaluation. In order to test the method experimentally, the particle diameters of different latices (homo- and copolymers) were measured and compared with the corresponding measurements obtained from ultracentrifugation and electron microscopy. The results are in good agreement.
    Notes: Zusammenfassung Auf der Grundlage der Theorien über die Lichtstreuung an kolloidalen Kugelteilchen (Mie, Zimm undDandliker) wurde eine Methode ausgearbeitet, mit der man aus Messungen von spezifischer Trübung und Brechungsinkrement den Radius und die Brechzahl der Teilchen ermitteln kann. Die Methode erfordert nur geringen experimentellen Aufwand und ist in der Durchführung sowie in der Auswertung der Messungen einfach zu handhaben. Zur experimentellen Überprüfung der Methode wurden die Teilchenradien bei mehreren Latices von Homo- und Copolymeren bestimmt und die Ergebnisse mit den entsprechenden Messungen in der Ultrazentrifuge und im Elektronenmikroskop verglichen. Die Übereinstimmung ist gut.
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  • 99
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    Colloid & polymer science 222 (1968), S. 192-192 
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 100
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    Colloid & polymer science 223 (1968), S. 1-5 
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Zusammenfassung Viele anorganische kristalline Substanzen sind polymer, meist nach ihrer chemischen Struktur dreidimensionale Netzwerke. Die anorganischen Polymeren, die nicht dreidimensional sind, verdienen besondere Beachtung, da sie ungewöhnliche mechanische Eigenschaften erwarten lassen. Polymerer Schwefel, linear im Bau, ist innerhalb eines sehr schmalen Temperaturbereichs elastisch. Cadmiumjodid, ein Flächenpolymeres, kann leicht gespalten werden und bildet dabei Lamellen so dünn wie 40 mikrons. Das Verhalten der Blättchen auf Zug sollte der Matrizen-Mathematik vonWeissenberg entsprechen, obgleich dies noch nicht demonstriert wurde. Goldjodid (AuI), beschrieben als ein lineares Polymeres, ist tatsächlich nicht linear. Die Au-I-Au-I-Zick-zacks, gebildet durch chemische Bindung, sind zu Ebenen metallisch miteinander gebundener Goldatome verknüpft, so daß das Ganze ein zweidimensionales Netzwerk darstellt. Die beobachteten mechanischen Eigenschaften sind mit dieser Struktur konsistent.
    Notes: Summary Of the many crystalline inorganic substances that are polymers, most are three-dimensional networks in their chemical structure. Those inorganic polymers that are not three-dimensional deserve special attention, since they may be expected to have unusual mechanical properties. Polymeric sulfur, a linear polymer, is elastic over a very narrow temperature range. Cadmium iodide, a sheet polymer, can readily be cleaved forming lamellar sheets as thin as 40 microns. The response of the sheets to tension would be expected to follow the trellis mathematics ofWeissenberg, although this has not been demonstrated. Gold iodide (AuI), which has been described as a linear polymer, is not in fact linear. The Au-I-Au-I-zig-zags formed by chemical bonds are fixed together by planes of metallically bonded gold atoms, so that the total structure is that of a two-dimensional network. The observed mechanical properties are consistent with this structure.
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