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Equation Methods (equation + methods)

Distribution by Scientific Domains
Engineering40%
Medical Sciences20%
Mathematics and Statistics20%

Kinds of Equation Methods

  • integral equation methods
    		•

    Selected Abstracts

    Evaluation of data for atmospheric models: Master Equation/RRKM calculations on the combination reaction ClO + NO2 , ClONO2, a recurring issue

    INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 9 2009
    David M. Golden
    Experimental data for the title reaction have been modeled using Master Equation/RRKM methods based on the Multiwell suite of programs. The starting point for the exercise was the empirical fitting provided by the NASA and IUPAC data evaluation panels, which represent the data in the experimental pressure ranges rather well. Despite the availability of quite reliable parameters for these calculations (molecular vibrational frequencies and a value of the bond dissociation energy of ClONO2, DH298(ClONO2) = 26.5 kcal mol,1, corresponding to ,H00 = 25.35 kcal mol,1 at 0 K) and use of RRKM/Master Equation methods, fitting calculations to the reported data was anything but straightforward. Using these molecular parameters resulted in a discrepancy between the calculations and the database of rate constants of a factor of ca 4 at, or close to, the low-pressure limit. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 573,581, 2009 [source]

    Individuals receiving addiction treatment: are medical costs of their family members reduced?

    ADDICTION, Issue 7 2010
    Constance Weisner
    ABSTRACT Aims To examine whether alcohol and other drug (AOD) treatment is related to reduced medical costs of family members. Design Using the administrative databases of a private, integrated health plan, we matched AOD treatment patients with health plan members without AOD disorders on age, gender and utilization, identifying family members of each group. Setting Kaiser Permanente Northern California. Participants Family members of abstinent and non-abstinent AOD treatment patients and control family members. Measurements We measured abstinence at 1 year post-intake and examined health care costs per member-month of family members of AOD patients and of controls through 5 years. We used generalized estimating equation methods to examine differences in average medical cost per member-month for each year, between family members of abstinent and non-abstinent AOD patients and controls. We used multilevel models to examine 4-year cost trajectories, controlling for pre-intake cost, age, gender and family size. Results AOD patients' family members had significantly higher costs and more psychiatric and medical conditions than controls in the pre-treatment year. At 2,5 years, each year family members of AOD patients abstinent at 1 year had similar average per member-month medical costs to controls (e.g. difference at year 5 = $2.63; P > 0.82), whereas costs for family members of non-abstinent patients were higher (e.g. difference at year 5 = $35.59; P = 0.06). Family members of AOD patients not abstinent at 1 year, had a trajectory of increasing medical cost (slope = $10.32; P = 0.03) relative to controls. Conclusions Successful AOD treatment is related to medical cost reductions for family members, which may be considered a proxy for their improved health. [source]

    On the BIEM solution for a half-space by Neumann series

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2007
    M. Y. Antes
    Abstract This paper presents an approach which allows the solution of elastic problems concerning a half-space (half-plane) with cavities by the boundary integral equation methods using Neumann's series. To evaluate the series terms at singular points, the regular representations of singular integrals for the external problems were proven and the regular recurrent relationships for the series terms, which can be calculated by any known quadrature rule, are obtained. The numerical proposed procedure was tested by comparison with known theoretical solution and the method convergence was studied for various depths of a buried cavity. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003
    Seppo Järvenpää
    Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A numerical-variational procedure for laminar flow in curved square ducts

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2004
    P. M. Hatzikonstantinou
    Abstract A new numerical method is presented for the solution of the Navier,Stokes and continuity equations governing the internal incompressible flows. The method denoted as the CVP method consists in the numerical solution of these equations in conjunction with three additional variational equations for the continuity, the vorticity and the pressure field, using a non-staggered grid. The method is used for the study of the characteristics of the laminar fully developed flows in curved square ducts. Numerical results are presented for the effects of the flow parameters like the curvature, the Dean number and the stream pressure gradient on the velocity distributions, the friction factor and the appearance of a pair of vortices in addition to those of the familiar secondary flow. The accuracy of the method is discussed and the results are compared with those obtained by us, using a variation of the velocity,pressure linked equation methods denoted as the PLEM method and the results obtained by other methods. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Risk factors for neuropsychiatric symptoms in dementia: the Cache County Study

    INTERNATIONAL JOURNAL OF GERIATRIC PSYCHIATRY, Issue 9 2006
    M. Steinberg
    Abstract Objective To investigate the probability of individual neuropsychiatric symptoms in dementia patients as a function of eight risk factors. Methods In the Cache County Study, we administered the Neuropsychiatric Inventory (NPI) to 328 dementia patients at baseline. Approximately 18 months later, we re-administered the NPI to 184 participants available for follow-up. Generalized estimating equation methods were used to model the probability of individual neuropsychiatric symptoms as a function of: gender, age, education, dementia type and severity, APOE status, time of observation, and general medical health. Results Women showed increased tendency toward anxiety, [odds ratio (OR) 2.22, 95% confidence interval (CI) 1.31,3.76] and delusions (OR 2.15, CI 1.22,3.78), but older persons of both sexes showed less tendency toward anxiety. Dementia severity increased the tendency toward hallucinations and agitation (OR 2.42, CI 1.81,3.23) and decreased risk of depression. Positive APOE ,4 status increased the tendency toward aberrant motor behavior (OR 1.84, CI 1.05,3.22). Among dementia diagnoses, those with Alzheimer's disease showed decreased tendency toward agitation (OR 0.58, CI 0.35,0.95), depression (OR 0.56, CI 0.33,0.96) and disinhibition (OR 0.46, CI 0.24,0.88). Later time of observation increased risk of aberrant motor behavior and delusions, and more serious medical comorbidity increased risk of, agitation, irritability, disinhibition, and aberrant motor behavior. Conclusions Gender, age, dementia severity, APOE ,4, dementia diagnosis, time of observation, and general medical health appear to influence the occurrence of individual neuropsychiatric symptoms. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Integral equation methods for scattering by infinite rough surfaces

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2003
    Bo Zhang
    Abstract In this paper, we consider the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane. These boundary value problems arise in a study of time-harmonic acoustic scattering of an incident field by a sound-soft, infinite rough surface where the total field vanishes (the Dirichlet problem) or by an infinite, impedance rough surface where the total field satisfies a homogeneous impedance condition (the impedance problem). We propose a new boundary integral equation formulation for the Dirichlet problem, utilizing a combined double- and single-layer potential and a Dirichlet half-plane Green's function. For the impedance problem we propose two boundary integral equation formulations, both using a half-plane impedance Green's function, the first derived from Green's representation theorem, and the second arising from seeking the solution as a single-layer potential. We show that all the integral equations proposed are uniquely solvable in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including an incident plane wave, the impedance boundary value problem for the scattered field has a unique solution under certain constraints on the boundary impedance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Regression Analysis with a Misclassified Covariate from a Current Status Observation Scheme

    BIOMETRICS, Issue 2 2010
    Leilei Zeng
    Summary Naive use of misclassified covariates leads to inconsistent estimators of covariate effects in regression models. A variety of methods have been proposed to address this problem including likelihood, pseudo-likelihood, estimating equation methods, and Bayesian methods, with all of these methods typically requiring either internal or external validation samples or replication studies. We consider a problem arising from a series of orthopedic studies in which interest lies in examining the effect of a short-term serological response and other covariates on the risk of developing a longer term thrombotic condition called deep vein thrombosis. The serological response is an indicator of whether the patient developed antibodies following exposure to an antithrombotic drug, but the seroconversion status of patients is only available at the time of a blood sample taken upon the discharge from hospital. The seroconversion time is therefore subject to a current status observation scheme, or Case I interval censoring, and subjects tested before seroconversion are misclassified as nonseroconverters. We develop a likelihood-based approach for fitting regression models that accounts for misclassification of the seroconversion status due to early testing using parametric and nonparametric estimates of the seroconversion time distribution. The method is shown to reduce the bias resulting from naive analyses in simulation studies and an application to the data from the orthopedic studies provides further illustration. [source]