Showing papers on "Constant (mathematics) published in 1970"
TL;DR: The model is based on the assumption that the cell cycle contains a Go‐phase which cells leave randomly with a constant probability per unit time, γ, which is a constant for all cells irrespective of their position in the cycle.
Abstract: The model is based on the assumption that the cell cycle contains a Go-phase which cells leave randomly with a constant probability per unit time, γ. After leaving the Go-phase, the cells enter the C-phase which ends with cell division. The C-phase and its constituent phases, the‘true’G1-phase, the S-phase, the G2-phase and mitosis are assumed to have constant durations of T, T1Ts, T2 and Tm, respectively. For renewal tissue it is assumed that the probability per unit time of being lost from the population is a constant for all cells irrespective of their position in the cycle.
The labelled mitosis curve and labelling index for continuous labelling are derived in terms of γ, T, and Ts. The model generates labelled mitosis curves which damp quickly and reach a constant value of twice the initial labelling index, if the mean duration of the Go-phase is sufficiently long. It is shown that the predicted labelled mitosis and continuous labelling curves agree reasonably well with the experimental curves for the hamster cheek pouch if T has a value of about 60 hr. Data are presented for the rat dorsal epidermis which support the assumption that there is a constant probability per unit time of a cell being released from the Go-phase.
254 citations
TL;DR: A constructive proof is given for finding constant feedback gains that stabilize a linear time-invariant controllable system.
Abstract: A constructive proof is given for finding constant feedback gains that stabilize a linear time-invariant controllable system. It is not necessary to transform variables or to specify pole locations.
163 citations
TL;DR: In this paper, the authors develop and test a "fair price" theory which is essentially contradictory to Weber's Law and show that as price levels rise, a constant price differential between brands becomes more important.
Abstract: This article develops and tests a “fair price” theory which is essentially contradictory to Weber's Law. As price levels rise, a constant price differential between brands becomes more important, r...
127 citations
TL;DR: In this paper, a theory is developed for calculating oscillations of harbours of constant depth and arbitrary shape, based on the solution of a singular integral equation, and numerical results have been calculated for rectangular and complex-shaped harbours.
Abstract: A theory is developed for calculating oscillations of harbours of constant depth and arbitrary shape. This theory is based on the solution of a singular integral equation. Numerical results have been calculated for rectangular harbours so as to check the accuracy of the method. Examples for wave amplification factor and velocity field for both rectangular and actual complex-shaped harbours are given.
119 citations
TL;DR: In this article, an analysis of the recently measured photon-proton total cross sections is performed and smooth fits are obtained and used to calculate, by means of the forward dispersion relation, the real part of the spin-averaged forward amplitude.
Abstract: An analysis of the recently measured photon-proton total cross sections is performed. Smooth fits to the cross sections are obtained and used to calculate, by means of the forward dispersion relation, the real part of the spin-averaged forward amplitude. The resulting predictions for the real part are given. At high energies, the fits to the present total cross-section data, together with the calculated real part, suggest the presence in the high-energy behavoir of an extra real constant in addition to what one would have predicted from Regge theory and the high-energy behavior of the imaginary part. This extra real constant, which is consistent in sign and magnitude with the Thomson limit, −αMN, could correspond to a fixed pole at J=0 in Regge-pole language. Possible ways to test the forward dispersion relation are discussed.
95 citations
TL;DR: In this article, the notion of the charge has been considered for the case of an ideally polarized electrode, and a definition of the total charge is given, equally applicable to ideally polarized and reversible electrodes, as the amount of electricity to be supplied to the electrode to keep the electrode potential constant when its surface is increased by unity and the composition of the bulk phases of the system is maintained constant.
81 citations
TL;DR: In this article, a queuing model with limited waiting room (buffer), batch (burst) Poisson arrivals, and a synchronous server (transmission channel) with constant service time (constant transmission rate) was studied.
Abstract: A queuing model with limited waiting room (buffer), batch (burst) Poisson arrivals, and a synchronous server (transmission channel) with constant service time (constant transmission rate) is studied. Using average burst length and traffic intensity as parameters, the relationships among buffer size, overflow probabilities, and an approximation to the expected queuing delay of each burst due to buffering are obtained. These relationships are represented in graphs which provided a guide to the buffer design problem. A simple example is given which applies these results to the design of a buffer system in a time-sharing computer system. Although the problem arose in studies of design of statistical multiplexers, the queuing model developed is quite general and may be useful for other industrial applications.
69 citations
TL;DR: In this paper, the authors generalized the path integral formulation of the spherical top to the case of a free particle moving on the manifold of a simple Lie group and showed that the finite propagator takes on the same form as the short time one except for the phase factor exp (-1/12iRt) where R is the constant scalar curvature of the group manifold.
Abstract: The calculations of Schulman (1968) on the path integral formulation of the spherical top are generalized to the case of a free particle moving on the manifold of a simple Lie group. It is shown that the finite propagator takes on the same form as the short time one except for the phase factor exp (-1/12iRt) where R is the constant scalar curvature of the group manifold.
55 citations
51 citations
TL;DR: A two-compartment model based on a well-perfused viscera region and a poorly perfused tissue region can simulate many of the general features of drug distribution kinetics such as concentration peaks that may occur at short times.
TL;DR: In this article, the authors investigated the inventory models in which customer good will is lost when stockout occurs and derived the optimal policies for the firm based on algebraic equations satisfied by the optimal parameter values.
Abstract: Investigation is continued of inventory models in which customer good will is lost when stockout occurs. Several models are formulated and optimal policies for the firm are derived conceptually i.e., algebraic equations satisfied by the optimal parameter values are determined. Both constant and distributed demand are considered, and it is shown that the same formulation applies to both.
TL;DR: In this paper, the pion-dilaton axial coupling constant Fσπ, the vacuum dilation tensor tensor constant fσ, and pion decay constant fπ satisfy F σ f σπ f π = 1 2.
TL;DR: In this paper, the spectral distribution of intensity of the apparent solar constant and the variations of transmission were investigated. And the authors showed that there is a close correlation between the variability of transmission and the apparent variability of the solar constant as it is presented in the volumes of the Astrophysical Observatory.
Abstract: The considerations contained in the following article are all based on the large number of observations of sun radiation and atmospheric transmission collected by the Astro-physical Observatory of the Smithsonian Institution. The author has shown that there is a close correlation between the variability of transmission and the apparent variability of the solar constant as it is presented in the Volumes of the Astrophysical Observatory. The relationship is explained on the basis of theoretical deductions presented by Dr R. Lundblad (1922) and by the present author (1921) at an early date. Further results, concerning the connection between the spectral distribution of intensity of the apparent solar constant and the variations of transmission, are based on the named theory. If the variability of the apparent solar constant is reduced to a value corresponding to a constant transmission, the remaining variability seems to coincide very closely with the standard error which can be expected in radiation measurements with our most accurate pyrheliometers. A short preliminary note is added concerning the wavelength dependence of atmospheric scattering as derived from the variability of the transmission for different wavelength intervals where no selective absorption occurs. DOI: 10.1111/j.2153-3490.1970.tb01522.x
TL;DR: In this paper, it was shown that force-free magnetic fields in resistive magnetohydrostatics are those for which α is constant in space and time, where α is defined by ▽ × B = α B.
TL;DR: In this article, the reference stress for various structures to be evaluated using standard techniques of numerical analysis using a simple case of a rectangular beam in pure bending is demonstrated using the simple case.
TL;DR: In this article, the effect of a constant thermal gradient on the transverse vibrational frequencies of a simply supported rectangular plate is investigated and bounds for the eigenfrequencies are obtained for various plate width-to-length ratios as functions of a parameter related to the temperature dependence of the modulus of elasticity of the material.
Journal Article•
TL;DR: In this article, a theory is developed for calculating oscillations of harbors of constant depth and arbitrary shape based on the solution of a singular integral equation, and numerical results have been calculated for rectangular harbors so as to check the accuracy of the method.
Abstract: A theory is developed for calculating oscillations of harbors of constant depth and arbitrary shape. This theory is based on the solution of a singular integral equation. Numerical results have been calculated for rectangular harbors so as to check the accuracy of the method. Examples for wave amplification factor and velocity field for both rectangular and actual complex-shaped harbors are given.
TL;DR: In this article, the authors present a linear model of cumulative damage, where failure is defined as the termination of the steady-state period, that is at the point of crack growth instability.
Abstract: An hypothesis of cumulative damage is presented that may be expressed mathematically as Σn÷Nf = constant where n is the number of cycles performed at a constant strain range and strain rate and Nf is the number of cycles to failure at the same strain range and strain rate.An initial experimental investigation at room temperature shows that, under constant strain-rate conditions, the load-sequence effect is removed, but the value of the constant is dependent on the definition of failure. If failure is defined as complete rupture the summation term is less than unity whatever the sequence of loading. Should failure be defined as the termination of the steady-state period, that is at the point of crack growth instability, then the summation term is greater than unity. This latter definition therefore leads to a linear law of cumulative damage that gives a doubly cautious prediction of life that is of obvious advantage to engineers.
TL;DR: In this article, the thermal equilibrium and feedback equations are combined, taking account of the inductance of the probe cables, to derive the governing equation for the unsteady probe current.
Abstract: The dynamic response of constant resistance anemometer systems is related to the thermal equilibrium of the probe during unsteady changes in surface cooling and also to the characteristics of the feedback system which supplies the heating current. This maintains the probe resistance and average temperature at approximately constant values. In this paper the thermal equilibrium and feedback equations are combined, taking account of the inductance of the probe cables, to derive the governing equation for the unsteady probe current. The probe inductance raises the order of this equation from first to second.
10 Feb 1970
TL;DR: In this paper, the authors define a large class of problems, when there is a positive lead time for delivery, which can be treated by the classical formulation with a single state variable, and all results which hold for inventory models with a constant delivery lag can be shown to hold also for the model.
Abstract: : In general, the single-product inventory model in which demands in successive periods are not independent is difficult to treat. The paper defines a large class of such problems, when there is a positive lead time for delivery, which can be treated by the classical formulation with a single state variable. All results which hold for inventory models with a constant delivery lag can be shown to hold also for the model. An application is made to a system in which demands are generated by part failure and in which a portion of these failures are repaired after a given (constant or probabilistic) time. (Author)
TL;DR: In this paper, the following conjecture of Erdos was proved: if f(n) is an additive function and 1 x Σ n≤x |f(n + 1) − f( n)| tends to zero as x tends to infinity, then f n is a constant multiple of log n.
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01 Jan 1970
TL;DR: In this paper, the authors studied Cauchy's problem with holomorphic data at the characteristic points of the hypersurface S carrying the data and showed that the solution u is algebroid at those points (but an equation with constant coefficients and constant data on a hyperplane constitutes an exceptional case).
Abstract: Cauchy’s problem with holomorphic data can be studied at the characteristic points of the hypersurface S carrying Cauchy’s data; (for linear equations, see [4], which improves [3; I]; for non linear equations, see Y. Choquet-Bruhat [1]). In general its solution u is algebroid at those points (but an equation with constant coefficients and constant data on a hyperplane constitutes, from this point of view, an exceptional case!). The solution u can be uniformed by a convenient map.
TL;DR: In this article, Stechkin's problem concerning the best approximation of an operator U by bounded linear operators is investigated for the case in which U is a functional and an upper bound is found for the discrepancy of the best approximation and properties of best approximating functionals are investigated.
Abstract: S. B. Stechkin's problem concerning the best approximation of an operator U by bounded linear operators is investigated for the case in which U is a functional. An upper bound is found for the discrepancy of the best approximation and properties of best approximating functionals are investigated. The results are used to study certain functionals related to the problem of finding the best approximation EN of the differentiation operator in C(S), and the value of EN is calculated for all cases in which the exact value of the constant in the corresponding Kolmogorov inequality is known.