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The duration of time between two successive births or between marriage and first birth is an indicator of the level of fertility of a couple. Potter and Parker (1964) and Singh (1961, 1967) have suggested the Type I Geometric as a distribution appropriate Or representing the length of interval to first conception leading to a live birth. Potter and Parker estimated the parameters of this distribution with the help of the first two moments. Majumdar and Sheps (1970) pointed out the limitations of these moment estimates and gave a method to Obtain maximum likelihood estimates, based on formulas which are too involved for solution without the help of a computer. Singh proposed a continuous probability distribution based on another set of assumptions for the above situation. He outlined a method to obtain best asymptotically normal estimates of the parameters. These estimates are obtained after several iterations starting from any set of consistent estimates. The objective of this paper is to show that it is relatively easier to obtain maximum likelihood estimates of the parameters of the continuous model, which describes the data on duration to first conception as well as does the discrete model. Simple expressions for the moment and maximum likelihood estimates with the corresponding covariance matrices are obtained. Application is made to three sets of data. [ABSTRACT FROM AUTHOR]

Place-of-birth-by-residence data, tabulated by age and sex for the same areal units in two successive censuses, have been used to estimate intercensal net migration flows. However, a fuller use of the same data permits the estimation of place-to-place flows. This paper describes a method for estimating intercensal migration streams from place-of-birth- by-residence data and illustrates its application with data on the white female native population of the United States. [ABSTRACT FROM AUTHOR]

If the pattern of fertility, mortality and interregional migration exhibited by the United States population during 1950-60 were to continue in the future, the proportions of persons in the various age groups and regions would fluctuate from decade to decade. These fluctuations would become less marked with time, however, and eventually all the proportions would stabilize at certain fixed values. This collection of values may be called a stable age by region composition corresponding to the given schedule of fertility, mortality and migration. The same phenomenon may be observed when individuals move between socioeconomic categories as, for example, socioeconomic status or educational attainment levels. The substantial differences between these various situations conceal remarkable similarities. In each case the continued operation of schedules of fertility, mortality and mobility between categories may result in a stable composition. The purpose of this paper is to shed some light on the nature of these stable compositions, on the interrelation between their various components, and on their relation to the patterns of fertility, mortality and mobility which generate them. [ABSTRACT FROM AUTHOR]

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New procedures are developed in this article for estimating parameters of the Pearsonian Type I curve which are particularly adaptive to factors influencing the pattern of age-specific fertility rates. It is shown that with this model the number of parameters required for the graduation and simulation of these rates can be reduced to only three--total fertility rate, mean and modal ages of fertility. The reduction in the number of fertility parameters offers considerable operational and analytical advantages, and makes the Pearsonian Type I curve particularly appropriate for the construction of a parametric model for fertility projections. In light of the results of empirical tests based on fertility data for Canada, the model's potential for birth projections appears quite promising. [ABSTRACT FROM AUTHOR]

The article presents abstracts of various manuscripts published in the December 1974 issue of the journal "Quality and Quantity." The article "Some Simple Mathematical Models for adoption Processes: The Case of the Comprehensive School Reform in Norway," reviews simple mathematical models which have been or may be used for adoption processes. Each model's role in the explanation process is analyzed. The case of the spread of the comprehensive school reform in Norway is used to illustrate an adoption process. The logistic, or chain-reaction model, and a normal model for independent adoption are emphasized. Another article "Models of Stratification Processes," presents certain mathematical models of the stratification process. These models are explicity concerned with the dynamics of stratification systems, and through their use it is possible to characterize time trajectories and also intra-system change. A foundation is laid for a comparative analysis of stratification systems and the analysis of historical change of any particular system. The mathematical models point to the limitation of current methodologies used in the analysis of stratification systems in that they explicitly or implicitly assume conditions of equilibrium, and employ procedures that obscure information about system change.

Considers the dilemma imposed by the cyclical majority problem in which an imputation set like (½, ½, 0), (0, ½, ½) precludes obtaining a single peaked preference set. Argument that the cyclically unstable outcome associated with such problems as how to divide one dollar among three persons operating with a majority rule is more of a mathematical dilemma than one ineluctably produced by individual utility maximizing behavior; Reason why the (½, ½, ½) imputation has been criticized as being stable.

We have determined unidirectional influxes by measuring rate of uptake between 0.5 and 1.0 min of incubation in 5 mm galactose.H-inulin was used to correct for galactose in residual mucosal solution. Influx was greatly depressed by removing Na from or adding 10 m phlorizin to the incubation medium. Influx was also greatly depressed by making the mucosal solution anaerobic during a 10-min preincubation period. The same severe inhibition of galactose influx by mucosal anaerobiosis also occurrend under conditions in which the epithelial cells did not gain Na. After taking into account the effect of the mucosal unstirred water layer, influxes could be normalized to a concentration of 1.0 mm at the membrane surface. It was estimated that at 1.0 mm the phlorizin-sensitive component of galactose influx was reduced 93% by 10 min of mucosal anaerobiosis. Unidirectional effluxes were estimated by subtracting steady-state downhill mucosal-to-serosal flux from influx. The ease of efflux was apparently augmented 2.8-fold by mucosal anaerobiosis. After 10 min of mucosal anaerobiosis, there was no longer any directional preference for movement of galactose across the brush border and there was no uphill transport, in spite of the persistence of a large Na gradient. These results provide strong evidence against the theory that ion gradients provide the major source of energy for directional preference and uphill transport. [ABSTRACT FROM AUTHOR]

Ionophoric material isolated by tryptic digestion of (Na+K)-ATPase containing electroplax membranes shows fluctuating discrete current levels in oxidized cholesterol membranes with conductance amplitudes ranging from 10 to 10 mhos, suggesting pore formation. The rate of pore formation is dependent on the imposed voltage. If the voltage is maintained for a short time (5 to 10 sec), pore formation is reversible, whereas permanent pores are formed when the voltage is maintained for more than 10 sec. At pH=7 the permeability ratio for sodium versus chloride is 5 and for potassium versus sodium, 1.7. The permeability of the ionophoric material is dependent on pH. At pH=6 a conversion takes place from more cation-permeable to more anionpermeable pores, suggesting that histidine plays a role in the permeation mechanism. A model is proposed to account for the observed ionophoric properties. [ABSTRACT FROM AUTHOR]

The partition of alkali cations and anions between an aqueous and an immiscible organic phase has been studied in the absence and presence of neutral and carboxylic ionophores of the valinomycin and nigericin types, respectively. Cation extraction into the organic phase was augmented considerably by the ionophores, and a cation specificity of K≧Rb>Cs≫Na was found for all the neutral ionophores tested. Evidence is given that the actual values of ion specificity are a function of the solvent polarity, especially for valinomycin where an inversion of the K/Rb specificity was observed. The ionophores examined have the following rank order of effectiveness for K extraction into a standard organic phase consisting of 70% toluene-30% n-butanol: valinomycin>18-crown-6≫trinactin>enniatin B≈dinactin>monactin>nonactin. The ion affinity and selectivity data thus obtained have been compared with data previously reported. In a toluene-butanol solvent, extraction of cations in the absence of ionophores occurs as ion pairs. On the other hand, the neutral ionophores extract the cations by the mechanism of complexation, with the lipophilic anions coextracted as free gegenionic species at lower ionophore complex concentrations. When the concentration of extracted cations exceeds 1×10 m, ion pairing between the ionophore complex and the anion occurs, and this tendency increases with increasing concentration and decreasing polarity of the organic phase. Anion pairing with the complexed cations is much less than for the free cations and this effect appears to be due to the larger distance of closest approach of the anion for the complexed cation. [ABSTRACT FROM AUTHOR]

The cation selectivity and its relation to the inward-going rectification of the immature egg cell membrane of a starfish, Nordora punctiformis, were studied and the following results were obtained. (1) When the external saline contains usual ion species the cell membrane at rest is predominantly permeable to K ions. The K chord conductance g depends on the electrochemical potential of K ions, Δ V=V−E and the external K concentration [K] by $$(\Delta V_h \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{ \doteq } - 15mV,\upsilon \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{ \doteq } 7mV)$$ . (2) The permeability sequence of monovalent cations and the permeability ratios P/P of the cell membrane at rest obtained with membrane tpotential measurements are, T1 (1.5)>K(1.0)>Rb(0.3 to 0.4)>NH(0.03 to 0.04)>Na, Cs. (3) Current-voltage relations obtained when the external solution contains Rb, Cs or T1 in addition to K show: (a) Rb and Cs decrease the K conductance and the rate of decrease becomes greater with an increasing hyperpolarization, thereby the inward-going rectification is reduced; (b) the membrane conductance shows an 'anomalous mole fraction dependence' in Tl-K media, i.e., the conductance becomes minimum at a certain mole fraction; and (c) the current-voltage relation often shows a transitiontype behavior suggesting that the membrane undergoes metastable states during an ncrease of hyperpolarization. [ABSTRACT FROM AUTHOR]

The operation of a seven-compartment model is described with respect to flows of Na within and across this system, simulating published results obtained on frog skin. The seven compartments represent: one outside and one inside solution compartment; the subcorneal space; the first reacting cell layer (1. RCL); the remaining cell compartment; the non-, or slowly exchangeable Na compartment; the extracellular space. Assuming reasonable volumes for the epidermal compartments and further chosing, by trial and error, appropriate rate constants, a set of seven simultaneous linear differential equations was solved by the application of the Continuous System Modeling Program (CSMP), using an IBM 1130 computer. Initial conditions for influx, backflux and net flux were taken which correspond to [Na]; [Na]=115 mm. Print-out data were obtained at 0.5-min intervals for 30 min, when steady states were obtained in 13 models studied, varying certain k's thus simulating actions of chemical agents (hormones; drugs). Simulation was achieved with regard to rate of influx, backflux and net flux, steady-state time (30 min), and electrical potentials. In addition, this approach gave detailed information on Na pool sizes and their variations with changes in k's. These results are compared to published data on frog skin and good agreement between operation of skin epidermis and model was found. [ABSTRACT FROM AUTHOR]

The stable population model is used to establish formulas expressing the effects of mortality change on population growth rates, birth rates, and age composition. The change in the intrinsic growth rate is shown to be quite accurately approximated by the average decline in age-specific death rates between age zero and the mean age at childbearing in the stable population. This change is essentially independent of the initial level of fertility in the population. Changes' in birth rates and age composition are shown to be simple functions of the age pattern of cumulative changes in mortality rates relative to an appropriately defined "neutral" standard. [ABSTRACT FROM AUTHOR]

This article discusses the family size utility function (FSUF), which portrays the relative strengths of preferences among family sizes, as held by an individual, couple, or group. Derivable from the FSUF are indications of motivation to seek or avoid additional children, indications which may prove useful for understanding fertility decisions and for predicting completed fertility. A method is described for assessing the FSUF with data obtainable by interview surveys, and case studies of actual FSUF's are presented. The article concludes with theoretical and empirical questions for further investigation of the FSUF. [ABSTRACT FROM AUTHOR]

Equations describing ten microfacies of Ste. Genevieve Limestone established previously on qualitative analysis of petrographic features are derived here in terms of measured lithic parameters. Mean values of each lithic parameter for each facies comprise independent variables with eigenvalues from discriminant analysis serving as coefficients for quasifunctional equations. This provides a unique quantitative expression for each qualitative microfacies, the dependent variable. Although these equations are not truly functional equations, they do provide explicit description of Ste. Genevieve Limestone facies. Quasifunctional equations form a necessary first step toward establishment of true functional equations describing unit lithology as functions of depositional parameters. Functional equations for lithic units offer a potential for an ultimate unification of classifications for all geologic materials. An immediate value of these quasifunctional equations resides in their explicit description and identification of subjective lithic classifications (facies), their utilization in comparative studies of lithic components in one or more stratigraphie units, their facility for an objective and automated digital reduction and graphic presentation of data, and their invitation for more careful examination and critical evaluation of natural relationships. [ABSTRACT FROM AUTHOR]

A rigorous treatment of the least-squares estimation of the parameters in petrologic materials balance equations is developed to take into account the uncertainties inherent in the chemical analyses. The choice of the optimal estimation procedure for a particular problem is dependent upon the extent of the petrogenetic understanding of the exact nature of the materials balance involved. Some of the complications entailed in obtaining least-squares estimates are illustrated by the examples of magmatic differentiation and metamorphic reactions. [ABSTRACT FROM AUTHOR]

The reduction of population growth rates through family planning programs is being attempted in many of the developing nations of the world. This activity lends itself aptly to mathematical modeling. Building from the well-known difference equation model of population growth, a model is constructed which integrates population dynamics, program activities, and resource consumption. The model may be used predictively to assess the outcome of various program activities. Alternatively, it may be used to determine the pattern of activities which yields the greatest reduction in births under the projected resource constraints. A further use of the model is the identification of the parameters to which predictions are most sensitive; such information provides valuable insights to those gathering the input data. The model is here applied to a family planning program currently in progress. An evaluation of the feasibility of that program's goals is provided, as well as information on limiting resources, data sensitivity, and the most important ages for contraceptive acceptance. [ABSTRACT FROM AUTHOR]

Evidence from Puerto Rico supports the hypothesis that the continuation rate has a decay form rather than a reciprocal form. As indicated in the literature, there was evidence that the continuation rate tends to vary not only with time but also with the age of the patient at acceptance. It was found that the fit of the continuation function could be improved substantially by making the effective decay rate an exponential function of age. Theoretical reasoning was presented to justify these empirical results. [ABSTRACT FROM AUTHOR]

The method of decomposition is applied to rates of natural increase in order to elucidate the role played by age composition in the growth of populations. A population's age distribution and fertility schedule are contrasted to those in a "stationary" population having the same mortality rates and having a fertility schedule equal to that of the observed population divided by its net reproduction rate. In this manner it is shown that about one-quarter to one-third of the growth of most current high-growth populations can be attributed to non-stationarity of their age distributions. This fraction will rise, as it has in most industrialized countries, if fertility is reduced and age distributions become middle-heavy. In projections of the 1963 Venezuelan female population with fertility rates declining by 2% and 1% annually, more than half of the growth (in numbers) that occurs prior to zero-growth attainment is contributed by non-stationarity of its intervening age distributions. [ABSTRACT FROM AUTHOR]

A technique for preparing contour maps is presented which has particular applicability for geophysical data. This technique derives from the assumption that each measured value is a sample from a statistical distribution which is taken to be valid in the area around that sample location. This distribution may be specified in the manner which best defines the relationship between the data and its spatial environment. Extending this principle to cover all areas to be mapped, and not just those measured, it is possible to predict values over a grid array of locations and hence to produce a contour map. Inherent in this simple procedure is: (i) the ability to adjust to the nature of the data being contoured; (ii) the elimination of edge effects; (iii) visual indication of the relative accuracy with which contours are located, at all points of the map; (iv) the automatic downgrading of data values which are in error; (v) the ability to contour combinations of measured data values without compounding errors; and (vi) a relatively simple extension to data spatially distributed in three dimensions. [ABSTRACT FROM AUTHOR]

Methods for calculating constant terminal-settling velocities (v) of spheres are examined for their validity and limitations of usefulness. A different approach is given which accurately predicts v for spheres over a wide range of hydraulic conditions based on past experimental work. The theory behind this approach is given along with the listing of a fortran program which directs the calculations of v. The practical limits of the author's method are stated, and tables of v may be generated from the program for common mineral densities over a range of sizes useful to sedimentologists. [ABSTRACT FROM AUTHOR]

The equations of Moseley for the volume and surface area of a coiled shell have been rewritten in their most general forms. The general volume equation has been tested with 15 gastropods and found to give satisfactory results wherever there are no significant ontogenetic changes in the shell geometry. The equations provide a means for calculating the carbonate efficiency of a coiled shell. With this parameter analyzed into its component parts, it has been possible to understand the relationships between aspects of shell calcification and environmental factors that affect calcium carbonate availability. Preliminary studies indicate that it also may be possible to discriminate morphologically between terrestrial and aquatic gastropods, the various gastropod modes of life, and higher taxonomic categories. These equations offer possibilities for other studies concerned with the ecology, paleoecology, and evolution of coiled shells. [ABSTRACT FROM AUTHOR]

Relative percentages of sand, silt, and clay from samples of the same till unit are not identical because of different lithologies in the source areas, sorting in transport, random variation, and experimental error. Random variation and experimental error can be isolated from the other two as follows. For each particle-size class of each till unit, a standard population is determined by using a normally distributed, representative group of data. New measurements are compared with the standard population and, if they compare satisfactorily, the experimental error is not significant and random variation is within the expected range for the population. The outcome of the comparison depends on numerical criteria derived from a graphical method rather than on a more commonly used one-way analysis of variance with two treatments. If the number of samples and the standard deviation of the standard population are substituted in a t-test equation, a family of hyperbolas is generated, each of which corresponds to a specific number of subsamples taken from each new sample. The axes of the graphs of the hyperbolas are the standard deviation of new measurements (horizontal axis) and the difference between the means of the new measurements and the standard population (vertical axis). The area between the two branches of each hyperbola corresponds to a satisfactory comparison between the new measurements and the standard population. Measurements from a new sample can be tested by plotting their standard deviation vs. difference in means on axes containing a hyperbola corresponding to the specific number of subsamples used. If the point lies between the branches of the hyperbola, the measurements are considered reliable. But if the point lies outside this region, the measurements are repeated. Because the critical segment of the hyperbola is approximately a straight line parallel to the horizontal axis, the test is simplified to a comparison between the means of the standard population and the means of the subsample. The minimum number of subsamples required to prove significant variation between samples caused by different lithologies in the source areas and sorting in transport can be determined directly from the graphical method. The minimum number of subsamples required is the maximum number to be run for economy of effort. [ABSTRACT FROM AUTHOR]

This article focuses on the new approaches in the philosophy of science. The style which until recently has dominated the scene the logic of science logical empiricism (LE) has been in the ascendant since the 20-ies and had its apogee in the U.S. of the 50-ies. The basic concern of the great philosophical systems of the 17th century was to account for the phenomenon of the "new science," This was the first and also the last time that physics or any other science, influenced the very perspective of genuine philosophizing. In the words of J.H. Randall: "With René Descartes, a mathematician a new factor enters into the stream of European thought, the fact of modern science, as something to be defended, understood and used." But it was not Descartes' physics nor his theory of research which made this impact, it was the mathematization of nature as dogmatized in the Cartesian metaphysics, and above all it was his "knowledge-anthropological solipsism." LE'S denial of the possibility of a praxiological theory of research as well as its denial of the possibility oil a philosophical anthropology of knowledge need no longer be taken seriously.