Function Of Independent Variables Research Articles

General approach to the sensitivity of the optics of an eye to change in elementary parameters with application to the Gaussian optics of a reduced eye

Optical properties of the eye, including the refractive compensation, for example, may change if there are changes in any of the components that make up the eye. The sensitivity to such changes isquantified via the derivative. This paper employs the reduced eye and Gaussian optics to illustrate a general method for the analysis of sensitivity in eyes. The method requires a clear statement of the dependent variable as a function of independent variables. A symbolism is offered that makes the function unambiguous. Sensitivities are determined for the fundamental optical properties,the transference and the corneal-plane refractivecompensation of a reduced eye to change in corneal power, curvature and radius of curvature and to change in axial length and index of refraction. Emsley’s reduced eye is examined in particular. Its corneal-plane refractive compensation has a sensitivity of 135 −135 D to change in refractive index, 1 − 2.7 D/mm to change in length and 135 −1/3 to change in corneal curvature when the other two independent variables are held fixed. The method has the potential to develop guidelines that are useful clini- cally.

General approach to the sensitivity of the optics of an eye to change in elementary parameters with application to the Gaussian optics of a reduced eye

Optical properties of the eye, including the refractive compensation, for example, may change if there are changes in any of the components that make up the eye. The sensitivity to such changes isquantified via the derivative. This paper employs the reduced eye and Gaussian optics to illustrate a general method for the analysis of sensitivity in eyes. The method requires a clear statement of the dependent variable as a function of independent variables. A symbolism is offered that makes the function unambiguous. Sensitivities are determined for the fundamental optical properties,the transference and the corneal-plane refractivecompensation of a reduced eye to change in corneal power, curvature and radius of curvature and to change in axial length and index of refraction. Emsley’s reduced eye is examined in particular. Its corneal-plane refractive compensation has a sensitivity of 135 −135 D to change in refractive index, 1 −2.7 D/mm to change in length and 135 −1/3 to change in corneal curvature when the other two independent variables are held fixed. The method has the potential to develop guidelines that are useful clini-cally.

Determinants of friction in soft elastohydrodynamic lubrication

Elastohydrodynamic lubrication (EHL) protects soft tissues from damage and wear in many biological systems (e.g. synovial joints, cornea of the eye, and pleural surfaces of the lung and chest wall). Among studies of lubrication of deformable solids, few have examined the effects of external loads, geometry, and material properties on EHL of soft tissues. To examine these effects, we studied the tribology of soft tissues in a two-dimensional finite element simulation of a thin layer of fluid separating a sliding rigid surface from a soft asperity or bump with an initial sinusoidal shape. We computed the frictional force, deformation of the solid, and change in fluid thickness as functions of independent variables: sliding velocity, normal load, material properties, and bump amplitude and length. Double-logarithmic regression was used to determine the exponents of the scaling relationships of friction coefficient and minimum fluid thickness to the independent variables. The analysis showed that frictional shear force is strongly dependent on velocity, viscosity, and load, moderately dependent on bump length and elasticity, and only weakly dependent on the bump amplitude. The minimum fluid thickness is strongly dependent on velocity and viscosity, and changes moderately with load, elasticity, amplitude, and length. The shape of the bump has little effect. The results confirm that the shear-induced deformation of an initially symmetrical shape, including generalizations to other symmetrical geometries such as quadratic or piecewise linear bumps, leads to load-supporting behavior.

Coronary Artery Z Score Regression Equations and Calculators Derived From a Large Heterogeneous Population of Children Undergoing Echocardiography

Clinical decision making in Kawasaki disease relies on measurements of the coronary arteries obtained by 2-dimensional echocardiography. Z scores relating measured values to independent variables are invaluable in ensuring the accurate and consistent treatment of patients with Kawasaki disease. The right coronary artery (RCA), left main coronary artery (LMCA), and left anterior descending (LAD) coronary artery were measured in 432 normal digital echocardiograms from a heterogeneous population of normal subjects aged 0 to 20 years. Linear regression analyses were performed relating the measurements to various functions of independent variables, including body surface area (BSA), height, and height. The adjusted R(2) and mean square error values were compared for each of the models, and the best model was chosen to create a Z score calculator. Using the model ln(measurement) = beta(1) + beta(2) x ln(BSA), the adjusted R(2) values were 0.638, 0.702, and 0.708 for the RCA, LMCA, and LAD coronary artery models, respectively, with mean square error < 0.0402. The calculation of accurate Z scores for coronary artery measurements in children can be accomplished using the Z-score calculator.

An infinite set of conservation laws for infinite symmetries

We consider partial differential equations of a variational problem admitting infinite-dimensional Lie symmetry algebras parameterized by arbitrary functions of dependent variables and their derivatives. We show that unlike differential systems with symmetry algebras parameterized by arbitrary functions of independent variables, these equations have infinite sets of essential conservation laws.

A comparative analysis of US toll policy

In the US, there is a long tradition of toll roads, beginning with the Lancaster Turnpike that was built at the end of the 18th century connecting Philadelphia and Lancaster. There are currently more than 300 toll facilities in the US, which is probably the largest number of toll facilities in the world. These facilities represent a wide range of conditions, from hypercongested facilities in large metropolitan areas such as New York City to toll highways in rural areas. The toll structures are equally diverse, ranging from multi-tier price structures with frequent user, carpool, and time of day discounts; to simpler structures in which the only differentiation is made on the basis of the number of axles per vehicle. The toll rates are typically set by the agencies that operate or own the toll facilities. The rules or formulas by which these tolls are determined are not generally available to the public, though it is safe to say that toll decisions are made taking into account technical considerations, as well as the all important criterion of political acceptability. However, data on toll rates and how they change by vehicle types and by some other attributes are readily available. The overall objective of this paper is to analyze the toll data from various facilities across the US to gain insight into the overall factors affecting the tolls. A more specific objective is to assess—though in a rather approximate fashion—if the tolls by vehicle type, relative to each other, are appropriate and consistent with economic theory. This is achieved by comparing tolls to approximate indicators of road space consumption and pavement deterioration. The literature review confirmed that this is the first time such research has been conducted which is an important first step toward an analysis of the efficiency of current toll policies. The analyses in this paper are based on a random sample of all toll facilities across the US. The toll dataset, which include toll rates for passenger cars, busses, and three different truck types, is assembled mainly from the available information on the web sites of various toll agencies. After cleaning the data, the authors used econometric modeling to estimate a set of ordinary least squares (OLS) regression models that express tolls as functions of independent variables. Three families of models were estimated: linear models, models based on expansions of Taylor series, and models based on piece-wise linear approximations to non-linear effects. The resulting models were analyzed to identify the salient features of current toll policies towards different vehicle types.

Modeling the Probability of Resource Use: The Effect of, and Dealing with, Detecting a Species Imperfectly

Resource-selection probability functions and occupancy models are powerful methods of identifying areas within a landscape that are highly used by a species. One common design/analysis method for estimation of a resource-selection probability function is to classify a sample of units as used or unused and estimate the probability of use as a function of independent variables using, for example, logistic regression. This method requires that resource units are correctly classified as unused (i.e., the species is never undetected in a used unit), or that the probability of misclassification is the same for all units. In this paper, I explore these issues, illustrating how misclassifying units as unused may lead to incorrect conclusions about resource use. I also show how recently developed occupancy models can be utilized within the resource-selection context to improve conclusions by explicitly accounting for detection probability. These models require that multiple surveys be conducted at each of a sample of resource units within a relatively short timeframe, but given the growing evidence from simulation studies and field data, I recommend that such procedures should be incorporated into studies of resource use.

Skurcz przetworczy wyprasek a warunki wtryskiwania

Results of experiments focused on assessment, in injection molding, of the effects of independent variables (input parameters) on dependent variables: longitudinal shrinkage (Sw), perpendicular shrinkage (Sp) (Fig. 2 and 3) and weights (m) of the moldings made of semi-crystalline polyoxymethylene (POM) or amorphous polystyrene (PS) were presented. Experiment design consisted of 27 systems investigated and 5 input parameters: mold temperature (Tf), injection temperature (Tt), clamping pressure (pd), cooling time (tch) and injection speed (vw) (Table 2 and 3). Diversification of values of perpendicular shrinkage along the way of plastic flow in mold cavity (Fig. 4) has been found. Statistic analysis of the results based on estimation of parameters of regression equations (2) describing the variability of dependent values investigated as the functions of independent variables (Table 6). Analysis of correlation was done as well and the results were presented in the form of matrix of correlation (Table 4 and 5). It results from the data presented that with the aim to control the shrinkage value and molding weight in the industrial practice it is most advantageous to change the clamping pressure as essential easy-to-change parameter.

An approximate closed form solution for pressure and velocity distribution in the cathode chamber of a PEM fuel cell

In this paper, an approximate technique is used to obtain pressure and velocity distribution in the cathode chamber of PEM fuel cells. The technique is based on polynomial profile approximation. The technique predicts two dimensional pressure and velocity distribution in closed form as a function of independent variables. The approximate solution developed compares reasonably with the rigorous numerical solution.

Assessment of nitrogen excess in an agricultural area using a nitrogen balance approach

A pilot study has been initiated to develop an approach for quantification of nitrogen excesses from agricultural activities that involve greenhouse farming in Kumluca Plain, Turkey. Detailed calculations utilizing the nitrogen balance method (NBM) were carried out at nine different locations within the plain over a time period of one year. The major contributing factors and governing operative mechanisms taken into consideration were nitrogen application rates both as organic and chemical fertilizers, irrigation water application practices, and nitrogen uptake by plants. The adopted approach yielded valuable information such as plant nitrogen uptake efficiencies, excess nitrogen, leaching rates and leachate nitrogen concentrations. Further, a site specific multiple linear regression model has been developed to estimate the ratio (N(leachate)/N(groundwater)) as a function of independent variables: farming age, excess nitrogen application and SEEPAGE Index Number. The negative sign of the model parameters implies that the ratio (N(leachate)/N(groundwater)) decreases as values of the independent variables increase. The adopted approach and the obtained results can beneficially be applied to similar sites to establish basic parameters of irrigation and fertilizer application operations.

Numerical simulation of polymer nanocomposites using self-consistent mean-field model

Clay-containing polymeric nanocomposites (PNC) are mixtures of dispersed clay platelets in a polymeric matrix. These materials show enhancement of physical properties, such as modulus, strength, and dimensional stability, as well as a reduction of gas permeability and flammability. The performance is related to the degree of clay dispersion (i.e., intercalation or exfoliation) and the bonding between the clay and the matrix. The main goal of this work has been to map the degree of dispersion as a function of independent variables (viz., magnitude of the interaction parameters, molecular weights, composition, etc.). In this paper, we present the results of the numerical analysis of the equilibrium thermodynamic miscibility using one- and two-dimensional (1D and 2D) models based on the self-consistent mean-field theory. In the limit, the 2D model reproduced the 1D model published results. The adopted 2D model considers the presence of four PNC components: solid clay platelets, low molecular weight intercalant, polymeric matrix, and end-functionalized compatibilizer. The simulations, with realistic values of the binary interaction parameters, were analyzed for potential exfoliation of PNC with a polyolefin as the matrix. The simulation results show that intercalation and exfoliation is expected within limited ranges of the independent variables. The presence of a bare clay surface (e.g., generated by thermal decomposition of intercalant or extraction by molten polymer) has a strong negative effect on the dispersion process. The simulation successfully identified the most influential factors, e.g., optimum ranges of the compatibilizer and the intercalant concentration.

Analysis of Laminated Anisotropic Cylindrical Shell by Chebyshev Collocation Method

The governing equations of a laminated anisotropic cylindrical shell problem are a system of partial differential equations. The boundary conditions will complicate the problem. Thus, it is hard to handle the governing equations in the form of functions of independent variables. Herein, Chebyshev collocation method is proposed to achieve the exact solution theoretically of such a difficult problem. Finally, two examples with numerical results are presented. The preciseness and efficiency of the proposed Chebyshev collocation method for laminated anisotropic shell problem are highlighted.

Influência da soma térmica e da chuva durante o desenvolvimento de laranjas-'Valência' e 'Natal' na relação entre sólidos solúveis e acidez e no índice tecnológico do suco

Este trabalho foi realizado com o objetivo de conhecer a influência que algumas variáveis meteorológicas exercem na razão entre sólidos solúveis totais e acidez total titulável ("ratio") e no índice tecnológico dos frutos da primeira florada das laranjeiras-'Natal' e 'Valência', na região de Bebedouro-SP, mediante a utilização de métodos estatísticos de regressão. Foram utilizados dados de amostragens de rotina para o processamento industrial durante 4 anos, os quais permitiram desenvolver equações de regressão linear e quadrática, com a soma térmica (graus-dia) como variável independente, e de regressão múltipla, utilizando graus-dia e chuva como variáveis independentes. A equação de melhor ajuste para o índice tecnológico foi a quadrática, enquanto para o "ratio" a equação linear apresentou o melhor ajuste. A temperatura do ar, representada por graus-dia, foi a variável que exerceu maior influência nos indicadores de qualidade dos frutos.

Causal Inference in Statistical Models of the Process of Socioeconomic Achievement

Typically, using data from a nonexperimental study, quantitative sociologists model one or more outcomes as a function of independent variables, interpreting the resulting parameter estimates as effects. This article compares the usual approach to causal inference in sociology with an alternative approach that builds explicitly on a counterfactual account of causation. The comparison is relevant because sociologists typically interpret (incorrectly) parameter estimates obtained using the first approach as supporting causal statements that are counterfactual. To make matters concrete, the author reconsiders an attainment model of Featherman and Hauser, who are interested in comparing the effects of family background on achievement, by sex and time. This analysis suggests the coefficients in the regressions of respondent's education and occupational status on background should not be interpreted as effects. However, because a child's sex is determined without regard for his or her subsequent achievements, sex may be viewed as randomly assigned, justifying treating sex as the cause and the background variables as covariates. Unfortunately, the way in which the data were collected preclude such a treatment.

Aging in wire insulation under multifactor stress

A fundamentally based chemical-thermodynamic multifactor stress aging functional relation requiring experimentally based constants is developed. The specific example presented is that of 120-V aromatic-polyimide-insulated wire. The stresses of water, temperature, and mechanical strain are included and electrical stress is considered. The results for over 2000 specimens are fitted to the theoretical trends. For a single independent variable function, the resulting relation reduces to the classical Arrhenius curve. The three independent variable relations presented here are applied to data from laboratory aging experiments that simulate insulation deterioration occurring in actual aircraft service. The results used in age categorization of US Navy aircraft are taken from wire specimens taken from active aircraft. The paradigm does not use ab initio based constants because of uncertainties in the theoretical development, two forms of which are presented. >

Independent variables in quantum mechanics

It is conjectured that the particle states of quantum mechanics are represented by functions of independent variables. These functions obey a linear differential equation which has an invariance group homomorphic to the inhomogeneous Lorentz group, thus giving a linear, Lorentz-invariant theory. Simple one-particle examples of equations which lead to a discrete particle spectrum are given, using both space–time variable, xμ, and sets of spinlike variables (pairs of complex numbers). Some of the examples have internal symmetry. No examples of realistic ’’many-body’’ particle theories are given, but we can deduce general characteristics. The differential equation must be of second or higher order to give an interaction. Products of single-particle states will be solutions of the equation and will form a complete set for widely separated particles. But products of one-particle states are not solutions of the equation for strongly interacting particles, and this permits the creation of particles. The origin of antisymmetry in such a theory is not clear.

Functions of Independent Variables in Research and Program Planning

Functions of Independent Variables in Research and Program Planning

The Formulation of Steam Properties for Digital Computer Application

Abstract Methods and equations are presented for approximating the properties of steam set forth in the Keenan and Keyes’ Steam Tables. Equations and functional relationships for derived thermodynamic properties as functions of basic independent variables are presented for compressed and saturated liquid, saturated and unsaturated vapor, and superheated steam. The thermodynamic properties, enthalpy and entropy, are described throughout while specific volume is determined only in the superheated steam region. Error plots of incremental differences from Keenan and Keyes’ values are shown as functions of the independent variables.