ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

Your email was sent successfully. Check your inbox.

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

Proceed reservation?

Export
Filter
  • Springer  (37,290)
  • 1970-1974  (31,733)
  • 1950-1954  (5,557)
  • 1935-1939
  • 1970  (31,733)
  • 1950  (5,557)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 1-24 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The usual method of tracer analysis for calculating the flow across a biological membrance is based on the assumption that the compartments on either side are well-stirred. Thus, the validity of the rate of flow determination is questionable for cases where the distribution of tracer is not homogeneous. In this study, a mathematical model is developed for the purpose of estimating the effect of slow mixing on the calculation of the flow rate. The model is applied to the measurement of the rate of flow of aqueous humor through the living eye by use of a fluorescent dye as a tracer. A transit time of several minutes for the passage of fluorescein through the posterior chamber and an extended period of nonuniform distribution of fluorescein in the anterior chamber was observed. The effect of slow mixing on the calculated flow rate is compared to rates derived from equations based on the assumption of rapid mixing. Aqueous flow rates determined by the two methods were found to agree to within ≈20%.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 25-43 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper presents a three-parameter model of the mechanism of dispersion of an indicator in the cardio-pulmonary system, based on the postulates that this dispersion can be described by the one-dimensional diffusion equation and that dispersion continues past the sampling site. The model is tested using indicator dilution curves obtained from dogs, and the coefficient of diffusion is thus measured. It is found that this coefficient increases in magnitude non-linearly with increasing blood speed.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 45-58 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Based on the ellipsoid model of the left ventricle and the helicoidal course of the left ventricular myocardial fibers, a theory has been developed for calculating the length of the individual myocardial fibers. Numerical solutions of the final equation show that when the left ventricle is distended, the increase in length of the myocardial fibers is not uniform throughout the thickness of the myocardial wall. It was shown that with increasing dimensions of the left ventricle, the distension of the myocardial fibers becomes smaller as one advances from the endocardium to the middle layer of fibers, whereas it increases as one advances from the middle layer to the epicardial layer. The mechanism by which this effect is brought about as well as its physiological implications are discussed.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 59-63 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In an open circuit gas washout determination the output of test substance is shown to be of the form ∑ i=0 ∞ A i λ i k on thekth expiration whereA i 〉0,i=1,2,... and 1 〉 λ1 ≥ λ2...≥ 0 provided the transition from inspiration to expiration has certain symmetry properties with the transition from expiration to inspiration. In general, no direct physical interpretation such as volume for theA t ’s or fraction of retained gas on expiration for the λ i is justified.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 71-78 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Previous studies by this author of the mathematical biology of automobile driving have emphasized only the biological aspects, except for such mechanical factors as the size of the car. Otherwise, the ideal case of an inertialess car was considered. In this paper the first step is made toward introducing the effects of the mass of the car and the side-slip of the tires when the direction of driving is even slightly altered and combining these with the previously studied biological aspects. Some tentative comparisons with available data are made.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 65-69 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract According to the occupation theory of drug receptor interaction, the response is a functionf of the number of receptors occupied by drug molecules. Considerable controversy exists regarding assumptions about this function. Without knowledge of the nature of the function, it is not possible to determine directly the rate constants, and hence the affinity constant, in the reaction between the receptor and an agonist drug. Instead, indirect determinations involving the use of antagonists have been employed, limiting the determination of affinity to those agents for which specific antagonists exist. The present paper discusses a method for the direct determination of affinity of an agonist drug. It is a “relaxation method,” i.e., the equilibrium is perturbed and the kinetics of the restoration process are studied. Assuming only thatf is non-decreasing and approximately linear over a limited domain of concentrations, it is shown that the change in response obeys first order kinetics, permitting a determination of the rate constants from the time course of the restoration process.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 79-81 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The basic postulate la, which governs the development of organismic sets, introduced previously (Bulletin of Mathematical Biophysics,31, 159–198, 1969), is generalized so as to contain also the rates of changes of the number and variety of differentQ-relations which determine an organismic set. It is thus brought closer to the Lagrangian principle in physics. It is pointed out that the postulate also provides a criterion of stability of an organismic set.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 155-172 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is presented in this paper for the in-vivo estimation of the nonlinear pressure-volume relationship of the human aorta. The method is based on nonlinear elastic reservoir theory and utilizes clinical data that can be obtained with a high degree of accuracy, namely stroke volume, end diastolic ventricular volume and aortic pressure trace data. The computational procedure is described and then carried out for six cardiac patients. A method for the estimation of instantaneous left ventricular volume during the ejection period based on the considered nonlinear elastic reservoir theory is also presented. The method is applied for the six cardiac patients cited and the results compared with those obtained for the same subjects by a method of estimation based on linear elastic reservoir theory described in a previous paper by the author (1969).
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 249-262 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Deakin (1967b) suggested that flow of blood might obey a law of minimal energy dissipation. The present paper presents a simpler derivation of Deakin’s equations pointing out several previously unrecognized features. It is shown that these equations are unlikely to be applicable. In particular, the solution obtained by Deakin and Jones (1968) does not yield a true minimum for energy dissipation. The solution for which energy dissipation is actually minimized is shown to possess features which render it unlikely to apply to a real flow.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 237-247 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf sm andf sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL p .
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 11
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 459-473 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract As was done by Sinclair and Ross (1969(, we consider a cellular population that consists initially (at time zero) ofN 0 newborn cells, all with the same volumev o. It is assumed that the occurrence of cell division is determined only by a cell’s age, and not by its volume. The frequency function of interdivision times, τ, is denoted byf(τ). If cell death is negligible, the expected number of cells,N(t), will increase according to the laws of a simple age-dependent branching process. The expression forN(t) is obtained as a sum over all generations; thevth term of this sum, in turn, is a multiple convolution integral, reflecting the life history ofvth generation cells (i.e., the lengths of thev successive interdivision periods plus the age of the cell at timet). Assuming that cell volume is a given function of cell age, e.g., linear or exponential, and that cellular volume is exactly halved at each division, it is possible to calculate the volume of a cell with a given life history, and thus the average cellular volume of the whole population as a function of time. If at time zero the volumes differ from cell to cell, the final equation must be modified by averaging over initial volumes. In the case of linear volume increase with age, a very simple asymptotic expression is found for the average cellular volume ast→∞. The case of exponential volume increase with age also leads to a simple asymptotic formula, but the resulting volume distribution is unstable. The mean cellular volume at birth and the second moment of the volume distribution can be calculated in a similar manner.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 499-520 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dynamic response of human musculo-skeletal framework is treated by (i) idealization of the musculo-skeletal framework as hybrid structural networks possessing feedback characteristics and then (ii) employing linegraph-flowgraph procedures for the feedback characterization of the hybrid structural networks. Topological procedures are used in which a “tree” of a network furnishes the skeleton upon which the “linkage” (muscle representing) members provide interaction. Feedback characterization (representing the sensitivity of the skeletal members to the tensile forces) is defined, between the internal “linkage” and “tree” members, by means of the flowgraph. Mikusinski operational calculus is used to facilitate representation of inertia effects by dynamic feedback characterization, with inclusion of initial conditions.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 13
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 539-561 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The representation of biological systems in terms of organismic supercategories, introduced in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 14
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 521-537 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The full implications of a statistical model for growth of a microbial cell population using cell mass as the index of physiological state have been examined by solving the partial differential integral equations resulting from the model. Calculations reveal that a lag phase is predicted during the initial stages of batch growth although no specific cellular mechanism for the phenomenon of lag had been incorporated into the model. The model predicts several situations of batch and continuous growth in which the population density and biomass concentration show opposing trends due to significant variation in the cell mass distribution with time.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 15
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 83-148 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Information treatment, especially in a natural medium, may be done by a random system: given an input, possible solutions are randomly selected and successively tested until the right one is found and then emitted. This paper is a mathematical study of this type of system and its use as a model of some natural (biological) systems. The theoretical development is illustrated by several examples of possible applications to biological cases. We study, under different assumptions, the distribution of the number of trials needed to treat the input, the distribution of the time for this treatment, and the distribution of the average amount of information treated in a trial or in a unit of time. We consider the case of error, and study some optimal conditions of operation and the occurrence of memory influencing the treatment of an input according to previously processed inputs.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 16
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 151-153 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 17
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 18
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 173-178 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The role of some inertial properties of the car, studied previously only for the case when the stimulus for the corrective turn is the perception of the angle between the direction of the car and the direction of a straight lane (Bull. Math. Biophysics,32, 71–78, 1970), is generalized to include such stimuli as the nearness to the edge of the lane and the anticipatory effect for a corrective turn, as well as the combination of all three stimuli. Conditions for stability of driving are deduced and discussed. They now depend on both biological parameters and such parameters as the position of the center of gravity of the car, its mass, and the side slip of the tires.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 19
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 179-195 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Description / Table of Contents: Résumé Pour le biologiste, la notion dedistance entre deux ou plusieurs éléments d’un ensemble est très utile car elle sert à mesurer laproximité, laparenté, laressemblance qui existe entre ces éléments ou parties selon le caractère auquel on s’intéresse (position géographique, situation chronologique, aptitudes, phénotypes, composition chimique etc...).
    Notes: Abstract Adistance between two mobiles performing a random walk in one dimension is defined. At a given time this distance is directly related to theprobability of encounter for the mobiles. This definition is used when the motion of the mobiles is a Wiener-Levy process, first in the case of an unrestricted random walk, then if a reflecting or absorbing barrier is introduced.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 20
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 197-213 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The qualitative effects of anisotropy and nonhomogeneity are considered in the evaluation of left ventricular stresses in the intact heart. Maximum stresses and their location are significantly dependent on the nonhomogeneity factors and to a lesser degree on anisotropy of the ventricular wall material. If the circumferential elastic modulus is assumed to vary in a parabolic manner through the wall thickness, maximum stresses occur within the endocardial layers, a result in qualitative agreement with experimental studies.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 21
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 215-218 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Under the assumption that there is complete mixing in the dead space a series of equations are given which give the values for a washout test of the functional component of the pulmonary bellows (without a dead space) in terms of the washout values of the bellows with a dead space.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 22
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 219-235 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Expressions are derived for the overall oxygen consumption and the O2 penetration depth into a tissue section in terms of the basic parameters, of the system under steady-state conditions. The approach differs from many previous analyses in so far as the oxygen molecules are regarded as reaching their sites of chemical assimilation by diffusion through extracellular fluid followed by bulk diffusion into irregular cells of significantly lower permeability. This “two-phase” model would seem to be compatible with the major experimental features of steady-state respiration, and gives a ratio of cellular to extracellular diffusion coefficients of the same low order as that found for inert gases under transient conditions. The greater oxygen penetration predicted by this model is discussed in relation to the survival of ischemic tissue and is shown to be consistent with data for myocardial infarction.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 23
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 263-278 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two models for a kidney-ureter system are considered: one model of one vessel in which a traced substance, undergoing exchange between the vessel and an external compartment, is emptying into the ureter; the second model of two approximately parallel, identical vessels in which a traced substance, undergoing exchange between each vessel and an external compartment, is emptying into the ureter. A single impulsive input of label into a vessel is assumed. For mathematical simplicity, the major conditions imposed on each system are: (1) rapid mixing transverse to a vessel axis and no mixing longitudinal to a vessel axis within the plasma; (2) small variation of the specific activity within the plasma in the longitudinal direction to a vessel axis; (3) constant flow rate of urine into the ureter and (4) constant exchange coefficients, tubule flow velocity and traced substance concentrations within individual compartments.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 24
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 279-291 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We use the concept of a layered wall, where each separate layer is to be homogeneous, isotropic, and incompressible, to derive stress-strain relations for the middle layer muscle ring at the transverse midsection of the left ventricle; a convenient method of formulation is that based on the elastic potential function. The hoop or circumferential stress in all three layers is found using dimensional and mechanical parameters derived earlier. The various parameters are expressed as Fourier series so that their behavior over a complete ventricular cycle is known analytically. The cases of simple elongation and what we termcurvilinear simple elongation are considered for the middle layer muscle ring strain, and the resulting stress-strain relations are derived. The results are compared with an incompressible rubber-like material known as a Mooney material.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 25
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 303-314 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Peaceman-Rachford finite difference method is applied to cylindrically symmetric, transient heat conduction problems in biological media. Inhomogeneous media and internal sources which vary in both space and time are permitted. Boundary conditions are satisfied without sacrificing high local resolution by means of an exponentially stretched grid. Computation time on a Philco 2000/210 computer is approximately 5 msec per grid point per time step.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 26
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 601-601 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 27
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 599-600 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 28
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. 581-598 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The energy cost of the left ventricle is quantitatively analyzed on the basis of the following assumptions: (1) The left ventricle is assumed to be an isotropic, homogeneous elastic, thick, spherical shell. (2) The ventricular wall is made up of a finite number of thin concentric shells. (3) The energetics of the left ventricle is in accordance with the second law of thermodynamics. An expression for the work done during ventricular contraction is derived according to the definition of physical work. The energy liberation during isovolumic contraction is formulated parallel to the concepts of heat production in skeletal muscle during isometric contraction. This expression gives the total work done per stroke in terms of mean systolic pressure, end diastolic volume, stroke volume and wall thickness during diastolic phase.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 29
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 32 (1970), S. i 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 30
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 6-16 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary This paper deals with a characterization of special cases when the distributive law is satisfied in interval arithmetic, a question first formulated byMoore [1]. To find a solution, the basic problem is subdivided into eight cases; in three of them distributivity ever holds, while in other three cases the law is failing. The conditions concerning the remaining cases are combined to a general characterization.
    Notes: Zusammenfassung Diese Arbeit behandelt die vonMoore [1] aufgeworfene Frage nach einer Charakterisierung der Sonderfälle, für die das distributive Gesetz in der Intervallarithmetik Gültigkeit hat. Das Ausgangsproblem wird in acht Fälle unterteilt, die einzeln behandelt werden; in dreien gilt das Gesetz immer, in weiteren dreien versagt es. Die Bedingungen, die sich für die beiden restlichen Fälle angeben lassen, werden zu einer allgemeinen Charakterisierung zusammengefaßt.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 31
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 57-70 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary A class of automata with tape has been defined and considered as recognition devices. Our automaton can use its working tape only as a buffer, i. e. in a “first-in-first-out” manner. Some modifications of the general model are considered, especially the deterministic, real-time version. The position in theChomsky hierarchy of the class of languages accepted by such automata and some operations with these languages have been investigated. Some results on decidability questions are cited.
    Notes: Zusammenfassung Es wird ein Automat mit Speicherband eingeführt und in seiner Eigenschaft als erkennender Automat untersucht. Er kann sein Arbeitsband nur als Puffer benutzen, d. h. was zuerst eingelesen wird, wird auch zuerst wieder ausgelesen. Es werden verschiedene Modifikationen des Grundmodells, insbesondere aber die deterministische, in Realzeit arbeitende Version betrachtet, sowohl hinsichtlich der Lage der durch den Automatentyp definierten Sprachklasse in derChomsky-Hierarchie, als auch das Verhalten dieser Sprachen gegenüber gewissen Operationen. Einige Resultate über Entscheidbarkeitsfragen werden zitiert.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 32
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 89-96 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 33
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 17-26 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary In the first part of this paper a method is given, which permits enclosing the first eigenvalue of positive completely continuous Operators in a separableHilbert space. The interval of enclosing, constructed by the orthogonal-invariants does not need arbitrary initial elements but needs knowledge of variety of the first eigenvalue. For numerical computation of the variety a method is proposed which supposes knowledge of estimation of the quotient of the first and second eigenvalue. The problem of enclosing higher order eigenvalues is treated in the second part of this paper.
    Notes: Zusammenfassung Im ersten Teil dieser Arbeit soll ein Verfahren angegeben werden, das es gestattet, den ersten Eigenwert eines positiven, vollstetigen Operators in einem separablenHilbert-Raum einzuschließen. Das mit Hilfe der Orthogonalinvarianten konstruierte Einschließungsintervall bedarf keinerlei willkürlicher Anfangselemente, benötigt aber die Kenntnis der Vielfachheit des ersten Eigenwertes. Zur numerischen Berechnung der Vielfachheit wird ein Verfahren vorgeschlagen, das die Kenntnis einer Abschätzung des Quotienten aus dem ersten und zweiten Eigenwert voraussetzt. Die Einschließung der höheren Eigenwerte wird im zweiten Teil der vorliegenden Arbeit behandelt.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 34
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 82-88 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 35
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 119-127 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary The construction of intervals of enclosing for higher order eigenvalues of positiveHilbert-Schmidt operators in a separableHilbert space is reduced to the problem of the interval of enclosing for the first order eigenvalue of a positiveHilbert-Schmidt operator.
    Notes: Zusammenfassung Die Konstruktion von Einschließungsintervallen für die höheren Eigenwerte positiverHilbert-Schmidtscher Operatoren in separablenHilberträumen wird auf die Aufgabe zurückgeführt, ein Einschließungsintervall für den ersten Eigenwert eines positivenHilbert-Schmidtschen Operators anzugeben.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 36
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 184-184 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 37
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 349-355 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary In 1967Cheney andGoldstein presented a paper on mean square approximation by generalized rational functions. The problem of uniqueness of the best approximation remained unsolved. In this paper it is shown, that there may be several different rational functions which are bestL p -approximation (1≤p〈∞) of a given function.
    Notes: Zusammenfassung In einer Arbeit vonCheney undGoldstein aus dem Jahre 1967 wurden die Probleme untersucht, die sich im Zusammenhang mit der rationalen Approximation einer gegebenen stetigen Funktion in derL 2-Norm stellen. In der vorliegenden Arbeit soll unter anderem die vonCheney undGoldstein offengelassene Frage der Eindeutigkeit der besten rationalen Approximation untersucht werden.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 38
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 394-394 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 39
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 312-323 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 40
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 332-332 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 41
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 71-81 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary Iteration methods are given for the solution of nonlinear equations in normed spaces requiring functionvalues and first-order divided differences. The latter may be replaced by derivations. The linear equations of each iteration step are solved only approximatively but this does not diminish the order of convergence.
    Notes: Zusammenfassung Zur Lösung von nichtlinearen Gleichungen in normierten Räumen werden Iterationsverfahren angegeben, die Funktionswerte und Steigungen erster Ordnung benutzen. Es ist möglich, die Steigungen durch Ableitungen zu ersetzen. Die linearen Gleichungen, die in jedem Iterationsschritt auftreten, werden nur näherungsweise gelöst. Dabei ist es wichtig, daß hierdurch keine Verringerung der Konvergenzgeschwindigkeit eintritt.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 42
    Electronic Resource
    Electronic Resource
    Springer
    Computing 5 (1970), S. 128-135 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary The intelligent behavior of a highschool student, who constructs triangles from three given pieces shows that he generates auxiliary points of a tree-like structure by means of geometric loci. The formalization of this leads to a system of points, geometric loci and rules. In each case the mechine is able to decide whether and how the triangle can be contructed and this leads to the decision-procedure we called the „Dreiecksalgorithmus”.
    Notes: Zusammenfassung Analysiert man das Verhalten eines intelligenten Schülers bei der Konstruktion eines Dreiecks aus drei gegebenen Stücken, so erkennt man, daß er mittels geometrischer Örter Hilfspunkte eines baumartigen Gebildes erzeugt. Eine Formalisierung dessen führt auf Listen von Punkten, geometrischen Örtern und auf ein Regelsystem. Die Maschine kann damit in jedem Fall entscheiden, ob und wie das Dreieck aus den gegebenen Stücken konstruierbar ist, und das ist das Entscheidungsverfahren, das wir „Dreiecksalgorithmus” genannt haben.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 43
    Electronic Resource
    Electronic Resource
    Springer
    Computing 6 (1970), S. 97-103 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Methode zur Definition und Charakterisierung der Zusammenhangs- und Repetitionsstruktur von Matrizen vorgeschlagen.—Im Anschluß an die Definition des “Vokabulars” der einzelnen Zeilen (Spalten) werden die numerischen Invarianten (Betti-Zahlen) eines simplizialen Komplexes bestimmt, der als der sogenannte “Nerv” des Systems der Zeilen-(Spalten-)Vokabulare erhalten wird. Die Berechnung erfolgt über die Inzidenzmatrizen des Nervs. Einige Hinweise auf Anwendungsmöglichkeiten und ein elementares Beispiel beschließen die Note.
    Notes: Summary A method is proposed for characterising the connectivity- and repetitivity-structure of matrices. After defining the “vocabularies” of the single rows (columns) we calculate the numerical invariants (Betti-numbers) of a simplicial complex, the “nerve” of the system of vocabularies, via incidencematrices.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 44
    Electronic Resource
    Electronic Resource
    Springer
    Computing 6 (1970), S. 104-106 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary In two previous papers [3] and [4] were deduced some statements for certain interval equations over the real number field concerning the existence and uniqueness of the solution and the convergence of iteration methods for the evaluation of the solution. This paper shows, how these statements and their proofs can be extended to analogous interval equations over the complex number field.
    Notes: Zusammenfassung In früheren Arbeiten [3] und [4] wurden für gewisse Intervallgleichungssysteme über dem Körper der reellen Zahlen Kriterien für die Existenz und Eindeutigkeit einer Lösung sowie die Konvergenz von Iterationsverfahren zur Bestimmung der Lösung bewiesen. Die vorliegende Arbeit zeigt, wie diese Kriterien und ihre Beweise zu verallgemeinern sind, damit sie auch für entsprechende Intervallgleichungssysteme über den komplexen Zahlen gelten.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 45
    Electronic Resource
    Electronic Resource
    Springer
    Computing 6 (1970), S. 107-120 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary Mathematical description of traffic flow has been tried repeatedly. Two types of theories are to be distinguished: Discrete traffic flow theories start from a system of differential equations for functionsx n (t) describing the routes of single cars. Continuous flow models require solution of a partial differential equation for the velocityv (x, t) and determination of trajectoriesx (t; c) of the velocity field thus obtained. In this paper these integrations for general initial and boundary conditions of a continuous flow model are performed. Treatment of a special case is added, yielding a flexible graphic method for solution of traffic flow problems. As an example of application, a frequently occurring traffic situation is analysed with this theory.
    Notes: Zusammenfassung Die Beschreibung des Kraftfahrzeugverkehrs in mathematischer Form ist mehrfach versucht worden. Es lassen sich zwei Typen von Ansätzen unterscheiden: Die diskreten Fahrzeugfolgetheorien gehen von einem Differentialgleichungssystem für die Bahnkurvenx n (t) der einzelnen Fahrzeuge aus. Die kontinuierlichen Strömungsmodelle verlangen die Lösung einer partiellen Differentialgleichung für die Strömungsgeschwindigkeitv (x, t) sowie die Ermittlung der Trajektorienx (t; c) im so entstandenen Geschwindigkeitsfeld, die als Bahnkurven der Fahrzeuge interpretiert werden. In der vorliegenden Arbeit werden für ein kontinuierliches Modell die genannten Integrationen bei allgeneinen Anfangs- und Randbedingungen geschlossen durchgeführt. Daran schließt sich die Behandlung eines Spezialfalles an, aus dem sich ein flexibles graphisches Verfahren zur Lösung von Kraftfahrzeugströmungsproblemen gewinnen läßt. Als Beispiel einer Anwendung wird ein im Verkehr häufig auftretender Effekt mit Hilfe dieser Theorie graphisch untersucht.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 46
    Electronic Resource
    Electronic Resource
    Springer
    Computing 6 (1970), S. 139-160 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein neues Stichprobenverfahren vorgeschlagen, das zur Untersuchung von zulässigen Gebieten in der Optimalsynthese dient. Die Methode ist gekennzeichnet durch einen größeren Wirkungsgrad der Stichproben und bevorzugt die Grenze und ihrer Nachbarschaft gegenüber dem Inneren des zulässigen Gebietes. Der Algorithmus des Irren-Prozesses und die Untersuchungsresultate werden beschrieben. Die Anwendung wird durch Beispiele illustriert. Die Resultate bei der Anwendung verschiedener Methoden werden verglichen. Die verwendeten Rechenautomaten waren GIER und ZAM-2 Computer.
    Notes: Summary A new method is proposed for the random checking of the region of admissible solutions of synthesis problems by means of digital computers. This method is characterized by increasing efficiency of random checking and by preference of the boundary and its neighbourhood to the interior of the region. The algorithm of the stray process is described. The paper contains also the test results of the influence of various parameters on the process. The application of the method is illustrated by examples. The results obtained by different methods are confronted. The computers used were the GIER and ZAM-2 computers.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 47
    Electronic Resource
    Electronic Resource
    Springer
    Computing 6 (1970), S. 161-172 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary By means of monoton decomposable operators,Collatz, Albrecht andSchröder have considered a variety of iterative methods, by which they get inclusion sets for the solution of system of simultaneous linear or nonlinear equations for example. It is shown, that these methods are special cases of basic iterative methods for equations with interval coefficients. In the concluding part of this paper a general convergence theorem in aRieszian-space is given.
    Notes: Zusammenfassung Vor allem vonCollatz, Schröder undAlbrecht wurden mit Hilfe des Begriffes des monotonen Operators verschiedene Iterationsverfahren betrachtet, welche Einschließungsmengen zum Beispiel für die Lösung eines linearen oder nichtlinearen Gleichungssystems liefern. Im folgenden wird der Zusammenhang zwischen diesen Verfahren und der Intervallrechnung hergestellt. Es zeigt sich, daß diese Verfahren als Spezialfälle in den auf Intervallbasis gebildeten Iterationsverfahren enthalten sind. Im abschließenden Teil der Arbeit wird ein allgemeiner Konvergenzsatz in einemRieszschen Raum angegeben.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 48
    Electronic Resource
    Electronic Resource
    Springer
    Computing 6 (1970), S. 342-348 
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Das Zunehmen der Kompression von wassergesättigten, porösen Medien läßt sich aus der Kontinuitätsgleichung, demDarcyschen Gesetz und einer passenden Druck-Ausdehnungsbeziehung herleiten. Theorien einer sekundären Verdichtung nehmen an, daß die tatsächliche Druck-Ausdehnungsbeziehung zeitabhängig ist. Eine Form dieser Charakterisierungsart ist ein System von linearen, viscoelastischen Modellen. Das ausgewählte Model besteht aus einem elastischen Element in Serie mit einer beliebigen Anzahl vonKelvin-Einheiten. Formuliert wird dieses System als Differential-Integral-Gleichung. Es wird ein endliches Differenzenschema entwickelt, in dem die beherrschende gewöhnliche Differential-Integralgleichung in ein Gleichungssystem übergeführt wird, das aus WärmeleitungsundEuler-Gleichungen besteht. Ein Stabilitätstheorem wird bewiesen.
    Notes: Summary The progress of compression of a water saturated porous medium is derivable from the equation of continuity,Darcy's law, and an appropriate effective stressdilation relationship. Theories of secondary consolidation assume that the effective stress-dilatation relationship is time-dependent. One form of this type of characterization is a system of linear viscoelastic models. The system chosen consists of an elastic element in series with an arbitrary number ofKelvin units. The formulation of this system is a differential-integral equation. The integral portions of the equation are a series of convolution integrals. A finite difference scheme is developed in which the single governing differential-integral equation is broken up into a system of equations of the heat conduction andEuler types. A stability theorem is proved.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 49
    Electronic Resource
    Electronic Resource
    Springer
    Meteorology and atmospheric physics 3 (1950), S. 84-97 
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Summary These past 25 years, sinceBenndorf [1] gave his theory of the electric field of the earth, the conception has been endorsed that the meteorological phenomena and especially the world-wide thunderstorm activity must be considered as the origin of the electric field of current. In this article the theory ofBenndorf, which is very general as regards the generator of atmospheric electricity, is applied to the thunderstorm activity being the current's source. It may be emphasized that many of the equations laid down here have already been developed byBenndorf for the case of the spherical condenser. Here the theoretical deductions are different: giving prominence to the field of flow, they proceed from the second equation of Maxwell and lead in a continuous development to the construction of an electro-technical equivalent circuit of the current in the spherical condenser. Proceeding from the technical notions the general physical deductions get much more distinctness. In addition, it can be shown that the space charges, which play the leading part in the electrostatic views on atmospheric electricity, have but little importance for the field of flow and have no influence on the current density or the field force. Thereby new prospects follow for the interpretation of the records of the electric field in a thunderstorm. The electro-technical equivalent circuit shows furthermore immediately that the world-time curve of the potential gradient on sea is not uninfluenced by the variable air-resistance on the mainland and that it reflects therefore only approximately the world-wide thunderstorm activity. Although this influence on the world-time daily variation is small — according to a rough valuation less than 17% — the desire arises for closer experimental and theoretical investigations about this problem.
    Abstract: Résumé Depuis queBenndorf [1] a donné, il y a 25 ans, sa théorie du champ électrique terrestre, l'opinion générale s'est de plus en plus affirmée que les phénomènes météorologiques et en particulier l'activité orageuse mondiale constituaient la source d'énergie du champ des courants électriques. Dans la présente étude, la théorie générale deBenndorf relative au générateur de l'électricité atmosphérique est appliquée plus particulièrement à l'activité orageuse considérée comme source de courant. Il faut remarquer que beaucoup d'équations établies ici avaient déjà été développées parBenndorf dans le cas d'un condensateur sphérique. La voie suivie est, il est vrai, différente, car en insistant sur la notion de champ de courant on part de la deuxième équation de Maxwell et on aboutit à une image électrotechnique du courant dans le condensateur sphérique. En utilisant les représentations de la technique, les principes physiques et les déductions gagnent beaucoup en clarté; il apparaît en outre que les charges électriques libres qui jouent un si grand rôle dans l'électrostatique atmosphérique sont très peu importants dans le champ de courant et n'exercent aucune influence sur la densité de courant ni sur l'intensité du champ. Cela ouvre quelques nouvelles perspectives sur l'interprétation d'un enregistrement du champ électrique lors d'un orage. De plus le schéma électrotechnique montre immédiatement que la courbe du gradient de potential sur mer en fonction du temps universel n'est pas indépendante de la résistance variable de l'air sur terre et ne reflète donc qu'approximativement l'activité orageuse mondiale. Bien que cet effet sur la variation diurne soit heureusement faible (probablement inférieur à 17%), il est à souhaiter que l'on poursuive sur ce point les recherches expérimentales et théoriques.
    Notes: Zusammenfassung SeitBenndorf [1] vor 25 Jahren seine Theorie des elektrischen Feldes der Erde schrieb, hat sich immer mehr die Auffassung durchgesetzt, daß das meteorologische Geschehen und speziell die Weltgewittertätigkeit als die Kraftquelle des elektrischen Strömungsfeldes anzusehen ist. In der vorliegenden Arbeit wird nun die bezüglich des luftelektrischen Generators recht allgemein gehalteneBenndorf-Theorie auf die Gewittertätigkeit als Stromquelle spezialisiert. Dabei soll gleich eingangs betont werden, daß viele der hier abgeleiteten Gleichungen bereits vonBenndorf für den Fall des Kugelkondensators entwickelt wurden. Der Weg der theoretischen Ableitung ist hier zwar ein anderer. Unter starker Betonung des Strömungsfeldes geht er aus von der zweiten Maxwellschen Gleichung und führt in stetiger Folge bis zur Konstruktion eines elektrotechnischen Ersatzschaltbildes der Strömung im Kugelkondensator. Durch das Anknüpfen an die technische Vorstellungswelt gewinnen einmal die allgemeinen physikalischen Ansätze und Ableitungen ungemein an Klarheit, zum andern kommt hier besonders deutlich zum Ausdruck, daß die Raumladungen, die im elektrostatisch luftelektrischen Denken die Hauptrolle spielen, im Strömungsfeld von ganz untergeordneter Bedeutung sind und gar keinen Einfluß auf die Stromdichte oder die Feldstärke haben. Es ergeben sich dabei einige neue Ausblicke auf die Ausdeutung einer luftelektrischen Feldregistrierung bei einem Gewitter. Ferner zeigt das technische Ersatzschaltbild unmittelbar, daß die Weltzeitkurve des Potentialgefälles auf See nicht unbeeinflußt von dem veränderlichen Luftwiderstand über dem Festland ist und somit nur in Annäherung die Weltgewittertätigkeit widerspiegelt. Wenn auch glücklicherweise dieser Einfluß auf den weltzeitlichen Tagesgang gering ist—nach roher Schätzung kleiner als 17%—, so entsteht doch der Wunsch, hier eingehendere experimentelle und theoretische Untersuchungen durchzuführen.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 50
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 1-36 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 51
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 37-44 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 52
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 45-54 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 53
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 55-70 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 54
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 71-78 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 55
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 79-80 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 56
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 81-99 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 57
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 99-99 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 58
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 100-107 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 59
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 130-134 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 60
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 108-129 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 61
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 135-139 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 62
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 140-156 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 63
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 161-174 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 64
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 157-160 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 65
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 183-187 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 66
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 67
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 210-220 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 68
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 69
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 221-234 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 70
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 235-240 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 71
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 241-254 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 72
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 284-307 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 73
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 265-283 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 74
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 255-264 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 75
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 308-312 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 76
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 313-329 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 77
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 330-344 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 78
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 345-353 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 79
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 54 (1950), S. 354-360 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 80
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 1-5 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 81
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 6-14 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 82
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 21-29 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 83
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 30-40 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 84
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 15-20 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 85
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 41-49 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 86
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 50-55 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 87
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 56-62 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 88
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 63-69 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 89
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 70-87 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 90
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 97-107 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 91
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 88-96 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 92
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 108-118 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 93
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 119-137 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 94
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 145-149 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 95
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 138-144 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 96
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 150-153 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 97
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 154-165 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 98
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 172-178 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 99
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 166-171 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 100
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 74 (1970), S. 179-182 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...