Showing papers on "Constant (mathematics) published in 1974"
366 citations
TL;DR: For quantum and classical fluids with only pairwise interactions, and under given conditions of temperature and density, the pair potential which gives rise to a given radial distribution function g(r) is unique up to a constant.
354 citations
[...]
TL;DR: In this paper, a threshold effect was added to the model, which yields the delay as a function of I(t), in order to allow for variations in the infection rate, and thus allow r, of the previous models, to be a function r(t).
Abstract: In the model discussed in the previous section, the function T(t) was prescribed a priori. Except for the case of constant delay, it is by no means clear how one would expect to know this function. In this section we add a phenomenon to the model, a threshold effect, which yields the delay as a function of I(t). In order to allow for variations in the infection rate, we now allow r, of the previous models, to be a function r(t). For example, it might be periodic to account for seasonal variations.
238 citations
01 Jan 1974
TL;DR: In this paper, the notion of empirical probability was introduced in the context of the "urn model" in which a population of observations which are related to certain measurable outcomes is assumed to be infinite and the observations are always reproducible according to a fixed prescription.
Abstract: In connection with the notion of probability we described the following situation: Assume we have a population of observations which are related to certain measurable outcomes. This population is taken to be infinite in the sense that the observations are always reproducible according to a fixed prescription, for example, an infinite series of throws of a die. From this population one now chooses a series of observations “at random”. If there are enough observations, then the relative frequencies of events related to the outcome under observation deviate in general only slightly from a constant value, which we have called the empirical probability (see p. 20). It is not easy to give empirical criteria for deciding when a sample from a population can be viewed as random. One often satisfies oneself with the somewhat vague formulation that a random sample has been realized when there is no reason to believe that the choice of any particular sample is more probable than the rest. In this connection, one often calls on an “urn model”. The urn, or better, its contents (for example, equal balls) represents the population and balls are then drawn from it, making sure that they are always “well-mixed” before each draw. The drawn ball is viewed as a random choice from the urn. We recall what has already been said about the urn scheme; in particular, to what these ideas correspond in the calculus of probability (see p. 27).
234 citations
TL;DR: In this paper, the Chandrasekhar-type Riccati-type difference equation is replaced by another set of difference equations, which are then used for recursive estimation in constant continuous-time linear systems.
Abstract: Certain recently developed fast algorithms for recursive estimation in constant continuous-time linear systems are extended to discrete-time systems. The main feature is the replacement of the Riccati-type difference equation that is generally used for such problems by another set of difference equations that we call of Chandrasekhar-type. The total number of operations in the new algorithm is in general less than with the Riccati-equation based Kalman filter, with significant reductions being obtained in several important special cases. The algorithms are derived via a factorization of increments of the Riccati equation variable, a method that can be extended to nonsymmetric Riccati equations as well.
215 citations
Journal Article•
141 citations
TL;DR: Most students of visual velocity perception implicitly assume that constant velocity is seen as such, but this notion was challenged and shown to be inadequate in four experiments, implying the existence of a perceptual concept of velocity which includes or presupposes a natural start.
Abstract: Most students of visual velocity perception implicitly assume that constant velocity is seen as such. This notion was challenged and shown to be inadequate in four experiments. A CRT-generated bright spot moved in a linear path according to different velocity time functions. Observers compared these movements pairwise as to their perceived constancy of velocity, or drew graphs describing perceived velocity along the track. Objects moving with constant velocity appear to move fast in the beginning and suddenly slow down to a much lower velocity. There is also a qualitative difference between the start phase and the rest. To be seen as constant, a movement must start smoothly with a certain acceleration and later level off to a constant velocity (natural motion). Such movements also look slower than others with the same average velocity. The results are taken to imply the existence of a perceptual concept of velocity which includes or presupposes a natural start. Consequences for velocity scaling, acceleration thresholds, and other motion perception studies, as well as relations to eye movements and conceptual problems, are discussed.
139 citations
TL;DR: The spectral density calculation of pulse trains resulting from the use of block codes is dealt with and the result obtained is particularly attractive since the finite-state machine model can be used to represent a broad class of encoding schemes of engineering interest.
Abstract: Block codes are multilevel codes of constant length whose codewords are the channel encodings of binary sequences of constant length. The spectral density calculation of pulse trains resulting from the use of these codes is dealt with. Under the assumption that the encoding be represented by a finite-state synchronous sequential machine, by means of homogenous Markov chain theory, the spectral density is evaluated in closed form. Both the continuous and the discrete spectral components are easily obtained as soon as the encoder functions are specified. The result obtained is particularly attractive since the finite-state machine model can be used to represent a broad class of encoding schemes of engineering interest. As an example, the spectral density is calculated in the case of the Franaszek MS-43 code.
121 citations
TL;DR: In this paper, the rotational diffusion coefficient of a liquid is related to the rotation correlation time τ 2 by means of the quasilattice model of liquids, and the results of the large-step random-walk theory of rotations are obtained.
Abstract: Self‐diffusion coefficients and rotational correlation times have been measured in several polar liquids by pulsed nuclear magnetic resonance techniques. Diffusion coefficients were measured for HCCl3, ClC6H5, HF, and HCl and relaxation times for HF. The self‐diffusion coefficient of a liquid is related to the rotational correlation time τ2 by means of the quasilattice model of liquids. The rotational diffusion equation and the Stokes–Einstein expression for the rotational diffusion coefficient are inadequate and are respectively replaced by the results of the large‐step random‐walk theory of rotational diffusion and an expression for τ2 based on the quasilattice model. An expression for τ2, obtained from the dynamical rotational coherence theory, is shown not to apply in the case of the spherical‐top molecule CCl4 which would be anticipated to have a small friction constant. The correspondence between calculated values of τ2 based on the quasilattice model and the observed rotational correlation times is...
110 citations
TL;DR: A constructive proof is given for easily finding constant feedback gains that stabilize a linear, time-invariant, discrete system.
Abstract: A constructive proof is given for easily finding constant feedback gains that stabilize a linear, time-invariant, discrete system. The results are directly applicable to initializing certain iterative methods that find steady-state gains for the discrete optimal regulator.
98 citations
TL;DR: The problem of finding the optimal, constant output feedback matrix for linear time-invariant multivariable systems with quadratic cost is reconsidered and simple formulae for the gradient matrix are developed and used in a Fletcher-Powell-Davidon algorithm.
Abstract: The problem of finding the optimal, constant output feedback matrix for linear time-invariant multivariable systems with quadratic cost is reconsidered. Simple formulae for the gradient matrix are developed and used in a Fletcher-Powell-Davidon algorithm. Computational results are presented.
TL;DR: In this paper, nuclear triple resonance (TRIPLE) experiments on free radicals in solution not only give considerable signal-to-noise improvement as compared to ENDOR, but also decrease the observed linewidth and give additional information about the number of protons contributing to a particular hfs constant.
Abstract: Electron nuclear triple resonance (TRIPLE) experiments on free radicals in solution not only give considerable signal‐to‐noise improvement as compared to ENDOR, but also decrease the observed linewidth and give additional information about the number of protons contributing to a particular hfs constant. The experimental setup is described and the results are discussed in terms of a phenomenological theory.
TL;DR: In this paper, a simple procedure is described to calculate the Anderson-Gruneisen parameter from the third-order elastic constants of a crystal and is used to evaluate the same for nine hexagonal metals and for the cubic magnesium oxide (MgO) in all the crystals, with the exception of beryllium.
Abstract: A simple procedure is described to calculate the Anderson-Gr\"uneisen parameter $\ensuremath{\delta}$ from the third-order elastic constants of a crystal and is used to evaluate the same for nine hexagonal metals and for the cubic magnesium oxide (MgO) In all the crystals, with the exception of beryllium, the relation $\ensuremath{\delta}=2\ensuremath{\gamma}$ is very nearly satisfied The relevance of these calculations to the anharmonicity in these crystals is discussed Anderson's theory has been used to explain the temperature dependence of the bulk modulus of the hexagonal metals magnesium, zinc, cadmium, and beryllium and the results are compared with experimental values
TL;DR: In this paper, the set of all finite order constant linear systems is parametrized as independent invariants for the equivalence relation, which defines two systems to be equivalent when they have the same impulse response.
TL;DR: In this paper, the Ideal Bose Einstein condensation is studied as a cooperative phase transition for arbitrary dimensionality and the correspondence with the n → ∞ limit of the n-vector model in the constant volume case and the n = − 2 limit in constant pressure case is discussed and precised.
Abstract: Ideal Bose Einstein condensation is studied as a cooperative phase transition for arbitrary dimensionality. The correspondence with the n → ∞ limit of the n-vector model in the constant volume case and with the n = — 2 limit in the constant pressure case is discussed and precised. The influence of a special type of disorder (random sources and sinks) is studied ; a sharp phase transition occurs with new critical exponents which are calculated and shown to violate some scaling laws.
IBM1
TL;DR: A simple model of thestorage hierarchies is formulated with the assumptions that the effect of the storage management strategy is characterized by the hit ratio, which is shown to be directly proportional to the logarithm of the systems capacity.
Abstract: A simple model of the storage hierarchies is formulated with the assumptions that the effect of the storage management strategy is characterized by the hit ratio fqnction. The hit ratio function and the device technology-cost function are assumed to be representable by power functions (or piece-wise power functions). The optimization of this model is a geometric programming problem. An explicit formula for the minimum hierarchy access time is derived; the capacity and technology of each storage level are determined. The opfimal number of storage levels in a hierarchy is shown to be directly proportional to the logarithm of the systems capacity with the constant of proportionality dependent upon the technolagy and hit ratio characteristics. The optimal cost ratio of adjacent storage levels is constant, as are the ratios of the device access times and storage capacities of the adjacent levels. An illustration of the effect of overhead cost and level-dependent cost, such as the cost per "box" and cos for managing memory faults is given and several generalizations are presented.
TL;DR: The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navier-Stokes equations introduced by Kraichnan (1958).
Abstract: The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navier-Stokes equations introduced by Kraichnan (1958, 1961). Instead of constant random coupling coefficients, white-noise time dependence is assumed for the MRC model. Like the Kraichnan model, the MRC model preserves many structural properties of the original Navier-Stokes equations and should be useful for investigating qualitative features of turbulent flows, in particular in the limit of vanishing viscosity. The closure problem is solved exactly for the MRC model by a technique which, contrary to the original Kraichnan derivation, is not based on diagrammatic expansions. A closed equation is obtained for the functional probability distribution of the velocity field which is a special case of Edwards’ (1964) Fokker-Planck equation; this equation is an exact consequence of the stochastic model whereas Edwards’ equation constitutes only the first step in a formal expansion based directly on the Navier-Stokes equations. From the functional equation an exact master equation is derived for simultaneous second-order moments which happens to be essentially a Markovianized version of the single-time quasi-normal approximation characterized by a constant triad-interaction time.The explicit form of the MRC master equation is given for the Burgers equation and for two- and three-dimensional homogeneous isotropic turbulence.
TL;DR: In this article, a pulse echo technique using thin line ultrasonics has been used to measure the variation with carbon content of austenite, and the results indicate the extent of the error which arises when the thermodynamic functions calculated from models involving constant interaction energies are compared with exparimantal thermodynamic data measured at constant pressure.
TL;DR: In this article, the limits of linear state variable feedback in modifying the dynamics of constant linear multivariable systems were derived from state space considerations, which were originally obtained by polynomial system matrix methods.
Abstract: The important theorem due to Rosenbrock, concerning the limits of linear state variable feedback in modifying the dynamics of constant linear multivariable systems, is obtained from state space considerations. This approach illuminates the results which were originally obtained by polynomial system matrix methods.
TL;DR: In this article, the relationship between Kawakita's constants and physical properties has been found out, and it was shown that the constant b is related with the yield strength σ 0 of the powder particles and apparent initial porosity Nao.
Abstract: Kawakita's experimental equation has been introduced from the relationship observed between pressure and volume in the case of piston compression.Although the cheracteristic constants a and b in Kawakita's eq. can be obtained by a graphical method, any clear relationship between these constants and physical properties has not been found out.The authors have carried out an experimental work on the hydrostatic compaction using several kinds of powders, i.e. electrolytic copper, electrolytic iron, reduced iron, atomized iron, molybdenum and tungsten.From the data obtained, it is found out that the constant a in Kawakita's eq. is nearly equal to the value of volume reducticn at infinitely large pressure, that is the initial porosity.On all the powders tested, two stages are recognized of the curve of Pb (V-V∞)/(Vao-V∞) versus (Vao-V)/(Vao-V∞), where P is the compacting pressure, b the constant, V-V∞ the volume of residual porosity, Vao-V∞ the volume of initial porosity and Vao-V the volume of reduced porosity.In the first stage that is the linear part of the curve, the constant b has a constant value. In this region, the constant b appears to be related with the yield strength σ0 of the powder particles and apparent initial porosity Nao.In the secondary stage that is the curved portion of the figure (Fig. 3), the constant b has not a constant value. In this region, the constant b appears to be related with σ0*, Nao and (Vao-V)/(Vao-V∞).The relationship between σt/P and 1/b has a clear linearity, and then this fact means that the constant b is related indirectly to the strength of powder particles.
TL;DR: In this article, a different, conceptually simpler solution to the same problem is proposed, based on an algorithm of the pole-shifting type, related to Remez's second algorithm.
Abstract: In a recent paper Thiran has proposed a method for the approximation of constant group delay in an equiripple manner, based on the method of Ulbricht and Piloty. A different, conceptually simpler solution to the same problem is proposed. The solution is based on an algorithm of the pole-shifting type, related to Remez's second algorithm. The choice of initial conditions is discussed and numerical solutions are given.
Patent•
24 Apr 1974
TL;DR: In this article, a high-velocity recirculating blower is used as a thermal energy source in an oven, which is maintained by varying the rate of blending of source of cooler air with the heated oven air.
Abstract: Inherent heating of the air in an oven by a high-velocity recirculating blower is used as constant rate thermal energy source. Constant temperature is maintained by varying the rate of blending of source of cooler air with the heated oven air. Automatic control of temperature is provided by a variable vent operated by a thermal expansion bellows. The bellows is slightly responsive to ambient temperature to compensate for variations thereof.
TL;DR: In this article, an analysis of the unsteady-state heat-conduction problem in isotachophoretic columns of circular cross-section is given, based on a linear variation of electrica conductivity with temperature and taking into account the effects of a finite wall thickness.
TL;DR: In this article, the asymmetric potential between two identical solutions of a 1:1 type electrolyte is observed when they are separated by a collodion membrane having different fixed charge densities in two sides of the membrane.
TL;DR: In this article, the temperature dependence of the anisotropy of the self-diffusion constant tensor in nematic DMBBA was determined by a multiple pulse NMR spin echo technique.
TL;DR: This paper extends the well known results for linear fractional programming to the class of programming problems involving the ratio of nonlinear functionals subject to nonlinear constraints, where the constraints are homogeneous of degree one and the functionals are homogeneously distributed to within a constant.
Abstract: This paper extends the well known results for linear fractional programming to the class of programming problems involving the ratio of nonlinear functionals subject to nonlinear constraints, where the constraints are homogeneous of degree one and the functionals are homogeneous of degree one to within a constant. Two rather general auxiliary problems are developed, and the relations between the solutions of the auxiliary problems and the solutions of the original problem are codified. Applications of the results for specific problems are also presented.
TL;DR: In this article, the constant gain feedback control to achieve desired closed-loop poles is used to minimize a given performance index, thus combining the pole-placement and optimal control design techniques.
Abstract: In pole assignment for multi-input systems, the constant gain feedback control to achieve desired closed-loop poles is not unique. This design freedom is used to minimize a given performance index, thus combining the pole-placement and optimal control design techniques.