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1 principles of physics (ie, the Navier-Stokes equations).
2 d generalization of a simplified equilibrium equation.
3 nd values predicted with the Stokes-Einstein equation.
4 nin degradation was modeled by the Arrhenius equation.
5 blem is reduced to a single algebraic matrix equation.
6 n dispersion calculated based on the BCS gap equation.
7  a single height- or area-based quantitation equation.
8 ne-cystatin C CKD-Epidemiology Collaboration Equation.
9 acy and feasibility of the established model equation.
10 ncertainty through a stochastic differential equation.
11  and could not be explained by the Arrhenius equation.
12 xact solution of linearized phonon Boltzmann equation.
13 mplementary information to the clinical risk equation.
14 that avoids direct solution of the Kohn-Sham equations.
15 consistency of the fluctuating hydrodynamics equations.
16 ompared by race using generalized estimating equations.
17  combines material balances and kinetic rate equations.
18 in all systems was estimated with allometric equations.
19 ng of the force-balance and myosin transport equations.
20 ally generate a system of reaction-diffusion equations.
21 g and compare them with results from Fresnel equations.
22 on zone (TZ) by using generalized estimating equations.
23 erestimation of D by employing the Nicholson equations.
24 l equations, for example, reaction-diffusion equations.
25 kers (eg, DTPA, iohexol), or estimated using equations.
26 dy fully coupled Poisson-Nernst-Planck (PNP) equations.
27 g to go through the complicated mathematical equations.
28 citonic reservoir described by a set of rate equations.
29 hich is not captured by standard firing rate equations.
30 hain, by numerically solving a set of matrix equations.
31 timated using Poisson generalized estimating equations.
32 were calculated using generalized estimating equations.
33 ved as self-consistent solutions of integral equations.
34 tors (k(obs) values) for corresponding power equations.
35 3; 95% CI, 0.68-0.79) than the Pooled Cohort Equations.
36 s were assessed using generalized estimating equations.
37  were conducted using generalized estimating equations.
38 s, bypassing the need to solve the Kohn-Sham equations.
39 ynamical evolution from partial differential equations.
40  were evaluated using generalized estimating equations.
41 an Health Survey 2011-12, and energy balance equations.
42 r and Fourier in Navier-Stokes-Fourier (NSF) equations.
43 ersion of this Article contained an error in Equation 1.
44 possible in the cubic non-linear Schrodinger equation (3NLSE) domain, and provides a further proof of
45 ation factor (beta of the simplified Simmons equation) across these SAMs with the corresponding value
46 to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency.
47       Models based on generalized estimating equations adjusted for baseline covariates and included
48 isson regression with generalized estimating equations, adjusting for age, sex, socioeconomic positio
49                            Neimark-Kiselev's equations afforded the evaluation of a pore volume varia
50 rom SPECT HMR via a simple linear regression equation, allowing use of the new cardiac-dedicated SPEC
51 ned molecular dynamics simulation and master equation analysis to elucidate the folding of an RNA pse
52 ugh a combination of the Boltzmann transport equation and ab initio calculations shows an excellent a
53                           Limitations of the equation and its use in predictions of distances in a va
54 he model takes the form of a dispersive wave equation and predicts canal responses to angular motion,
55 asurements were mapped against the consensus equation and receiver operating characteristic (ROC) cur
56 l provides a number of ordinary differential equation and stochastic numerical solvers for single-com
57 nse experiment, this paper used the logistic equation and the Gompertz equation to fit the growth pre
58 , and differences between the SAFEHEART risk equation and the other 2 were significant (P=0.023 and P
59 n rate could be represented by the Arrhenius equation and therefore can be controlled by the temperat
60 rlattices by solving the Boltzmann transport equation and using the Beckman-Kirchhoff surface scatter
61 rably with calculated values from the Levich equation and with data obtained using more typical, nong
62               We combined the Hodgkin-Huxley equations and a 36-state model of gap junction channel g
63  the transplant center, including estimating equations and clearance measurements.
64                       Generalized estimating equations and Cox regression were used to assess associa
65 y using multivariable generalized estimating equations and evaluated the impact of adjusting for surv
66 malism includes exact treatment of Maxwell's equations and exact treatment of the interaction among t
67                       Generalized estimating equations and nonparametric bootstrap procedure for clus
68 y numerically integrating the nonlinear rate equations and performing linear stability analysis, reve
69 egression models with generalized estimating equations and robust variance estimators and included ad
70 lk equations into free- and bound-associated equations and solving resulted inverse problem by using
71  simulated and analysed by solving Laplace's equation, and the deformation of the medium during the t
72 score, the Pulmonary Hypertension Connection equation, and the Mayo Clinic model.
73 ing multiple linear and nonlinear mathematic equations, and the significance of sex was assessed usin
74                   The generalized estimating equation approach was used to deal with correlated data
75 ession models under a generalized estimating equations approach to explore the relationship between A
76  measurements that obey the Michaelis-Menten equation are well established.
77 ature and formulations such as the Arrhenius equation are widely used in earth system models.
78                                    Different equations are appropriate depending on whether a mediato
79 emperature ranges of the data from which the equations are derived; and (4) model performance is stro
80                                    The model equations are either derived purely from first physical
81  is suppressed and the standard Wilson-Cowan equations are formally recovered as long as external inp
82 red by two hand-helded analyzers: conversion equations are needed to compare the FENO values between
83 re described by ultrarelativistic Dirac-like equations, are of a significant current interest from bo
84               Joint static allometry scaling equation as sub-model is nested within the genetic effec
85 ponse, we here analyze a set of differential equations as well as simulations employing the cellular
86          Numerical solution of the diffusion equation, as well as ab initio calculations, support our
87 ate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear tur
88                                A biophysical equation (Augmented Growth Equation) was previously show
89                  We use a reaction-diffusion equation based model of tumour growth to investigate how
90 roperties of solutions for systems of linear equations based on a random choice of [Formula: see text
91  the USEPA's current hardness-based criteria equations but with DOC, pH, and hardness as the independ
92 isson regression with generalized estimating equations calculated the relative risk (RR) and 95% conf
93  Rice-Ramsperger-Kassel-Marcus (RRKM)-master equation calculations correctly predict the direction of
94                       The simple generalized equation can be expressed as Wh = p(ln h)(q), where h is
95 Neumann and Wigner showed that Schrodinger's equation can have bound states above the continuum thres
96 reement with predictions of the excess phase equation central to the theory of lasers under OF.
97 quation is shown to approach the phase field equation commonly used to simulate the above processes.
98 erreporter phenotype; generalized estimating equations compared 6MP intake by self-report and MEMS.
99 tic problem and its reduction to simple rate equations; computation of binding rate constants; quanti
100 described non-Michaelis-Menten kinetics with equations containing parameters equivalent to kcat and K
101 ally take the form of nonlinear differential equations depending on parameters; dynamical systems the
102 e we propose a Bayesian approach based on an equation derived with the total quasi-steady-state appro
103 pair of first order, non-linear differential equations, derived from the Lotka-Volterra model (Predat
104 mbination with the phenomenological Langevin equation describing the periodic conformational changes.
105 ng and rejuvenation, through a set of simple equations describing excitations in the PEL.
106           Based on the experimental results, equations describing the amount of damage caused by each
107                                  Calibration equations did not capture dependencies on body mass inde
108                            The Pooled Cohort Equations discriminated MI risk and were moderately cali
109                              A single global equation embodying these relationships then unifies the
110 solution to the spherical diffusion-reaction equation enabled testing of several models for the react
111 ocused on the risk side of the substance use equation: escalation of substance use.
112                       Generalized estimating equations estimated relative risks per interquartile-ran
113                 In our Ordinary Differential Equation examples the crossing of infinity occurs instan
114                  Here, we show that a single equation fails to qualitatively capture diverse pairwise
115                                        A new equation for converting EC50 into TEAC values and TEAC i
116                    Solving the Fokker-Planck equation for high-dimensional complex dynamical systems
117 ogy/American Heart Association Pooled Cohort Equation for the composite outcome and incident heart fa
118 redicted from the behavior of the replicator equation for the modified game.
119 ame is different from that of the replicator equation for the modified game.
120  solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Poschl-Teller potential
121  statistical approach to derive a prediction equation for the partial pressure of CO2 (pCO2 ) in lake
122              To develop spirometry reference equations for adult Hispanic/Latino background groups in
123 s were derived using the GLI-2012 prediction equations for African Americans.
124  the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled wit
125 ing cystatin-C-based eGFR in risk prediction equations for CKD progression and all-cause mortality an
126                       Generalized estimating equations for logistic regressions with covariate adjust
127  (ACCORD, n=9635; 2001-09) and validated the equations for microvascular events using data from the D
128 en to the complex highly nonlinear transport equations for non-conserved variables that arise from th
129 nt regime, we derive a reduced closed set of equations for population-level quantities in the station
130               Numerical integration of these equations for prescribed values of the parameters and in
131                                          The equations for the discrimination of seasonality was obta
132 und to produce background-specific reference equations for the predicted value and lower limit of nor
133 d solve the systems of ordinary differential equations for the two lower-order moments of the stochas
134 ogy/American Heart Association Pooled Cohort Equations (for fatal or non-fatal myocardial infarction
135 f mathematical models by way of differential equations, for example, reaction-diffusion equations.
136 ivariate longitudinal Generalized Estimating Equation (GEE) model, each 10 mg increase in prednisone
137 pecific analyses, and generalised estimating equations (GEE) for the global (ie, any) pathogen analys
138 e was conducted using generalized estimating equations (GEE) to examine the association of SCT with H
139 ted by the well-known generalized estimating equations (GEEs) for longitudinal data analysis, we focu
140     Application of an approximate van't Hoff equation gives the temperature dependence of Henry's con
141                                          The equations governing the angular momentum of the ball rel
142  are used to rigorously derive the continuum equations governing viscous, liquid-like granular flow.
143                                          Our equations had better discrimination and calibration than
144                                          All equations had moderate internal and external discriminat
145                         The Michaelis-Menten equation has been widely used for over a century to esti
146 For well over one century, the Hertz-Knudsen equation has established the relationship between therma
147                                    Reference equations have been established for Mexican Americans bu
148 nostic information independent of the REVEAL equation, improving the C statistic from area under the
149                        To validate consensus equation in a perioperative setting analyses of cases of
150 ration measurements and the phenomenological equation in this article, we provide a general and pract
151 pth averaging of three-dimensional transport equations in a second-order asymptotic analysis.
152 an be recapitulated by specific mathematical equations in embryos and larvae and that accurate dentic
153 uster-adjusted Poisson generalised estimated equations in the intention-to-treat population after 58
154 ied by numerically solving the Navier-Stokes equations in the moving wall domain with our validated f
155  be described by a large hierarchical set of equations in the transient regime, we derive a reduced c
156 e static equilibrium state of Lotka-Volterra equations in which bacterial growth is exactly balanced
157 elative to a CPU-based ordinary differential equation integrator.
158 lgorithms included the decomposition of bulk equations into free- and bound-associated equations and
159 arameterized system of ordinary differential equations into regions for which the system has a unique
160     There was high interobserver agreement [(Equation is included in full-text article.)= 95.3%, (95%
161 ull-text article.)=97.5%) compared with 2D ((Equation is included in full-text article.)=54.5%) [diff
162  anastomosis more often with 3D ultrasound ((Equation is included in full-text article.)=97.5%) compa
163          Therefore, a novel rate of reaction equation is proposed to characterize the hydrolysis of u
164  roughly 2.5 mum, our generalization of this equation is shown to agree remarkably well with full-sca
165 nsforming solids, and the discrete governing equation is shown to approach the phase field equation c
166          A generalized nonlinear Schrodinger equation is used to describe the coupled dynamics of opt
167         The corresponding system of kinetics equations is solved analytically to obtain concise expre
168 egral of motion of the nonlinear Schrodinger equation, keeping this ratio constant is a key principle
169 yzed using univariable generalized estimated equations logistic regression models accounting for inte
170                       Generalized estimating equations logistic regression was used to assess T1, T2,
171 s not superior to clinic BP, risk prediction equations may be useful for identifying the subgroup of
172  diameter (PM10), and generalized estimating equations methods adapted for low-prevalence exposure, w
173 rare diseases via the generalised estimating equation model in a modified intention-to-treat populati
174 minimal one-dimensional partial differential equation model that reproduced the range of observed mot
175  comparisons, and the generalized estimating equation model to control for nonindependence.
176 tion-level dynamics (in an integrodifference equation model).
177            We also perform conventional Hill equation modeling and illustrate how comparatively limit
178 7 from 4 US communities), we used structural equation modeling to estimate the association between se
179 ectional data were analyzed using structural equation modeling to examine the associations among EAP,
180  used tree-ring isotopic data and structural equation modeling to examine the concurrent and interact
181                         Employing structural equation modeling, a descriptive-correlational study was
182 sed on mixed-effects modeling and structural equation modeling, low-intensity fire increased growing-
183                             Using structural equation modeling, we modeled illness and medication bel
184 atios (i.e. effect size) and used structural equation modelling (SEM) to achieve a system-level under
185                     In controlled structural equation modelling analyses, medication adherence partly
186                           We used structural equation modelling analysis to estimate whether medicati
187                           We used structural equation modelling on 341 older adults to establish thre
188 ng and mammal abundances, and use structural equation modelling to compare competing trophic cascade
189 s, we use logistic regression and structural equation modelling to show pathways and mediators.
190                           We used structural equation modelling to test the importance of direct and
191              To do so, we coupled structural equation modelling with 20 years of mark-recapture and n
192 aridity gradient using multilevel structural equation modelling.
193                       Generalized estimating equation models assessed lung function and symptom relat
194                      Continuous differential equation models do not recapitulate this phenomenon.
195 arch, genetic-relationship-matrix structural equation models included Cholesky decomposition, common
196 ally, genetic-relationship-matrix structural equation models present a framework for modeling shared
197  Multiple regression analyses and structural equation models were applied to determine the associatio
198                       Generalized estimating equation models were used to account for correlation bet
199             Piecewise generalized estimating equation models were used to compare groups and to ident
200          Multivariate generalized estimating equation models were used to determine the association o
201 ioeconomic status and wealth, and structural equation models with maximum likelihood to test mediatio
202 entified in bivariate generalized estimating equation models, and maintained significance of P </= .1
203               Using moving window structural equation models, we show that substantial changes in eco
204 llular dynamics through partial differential equation models.
205 ng beyond it in a broader range of evolution equation models.
206 ilds dynamic (based on ordinary differential equation) models, which can be used for mechanistic inte
207                        Ordinary differential equations (ODEs) with polynomial derivatives are a funda
208 hich enables us to reconstruct its dynamical equation of motion.
209 rough the Fluctuation Theory-based Tait-like Equation of State (FT-EoS).
210 HD approach includes correlations in the the equation of state self-consistently, satisfies sum rules
211 unctional theory and forces derived from the equations of Ehrenfest dynamics that depend instantaneou
212                                          The equations of motion for the proton operators are derived
213 ppears in the Heisenberg picture as nonlocal equations of motion.
214                               The regression equations of these parabens exhibited good linearity (r(
215 r constraining both thermal conductivity and equation-of-state models.
216 rmal conductivity and LEOS for Au/Al release equation-of-state show good agreement with data after 15
217                                         Rate equations on fibril disappearance are deduced from a sim
218 es to the solution of a partial differential equation (PDE).
219 s of individual trees and find that a single equation predicts stem diameter from these two variables
220 re analyzed using the generalized estimating equations procedure.
221 tatistics followed by generalized estimating equation regression modeling.
222               We used generalised estimating equation regression to study moderation of differences b
223  coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mecha
224            This success is notable given the equation's simplicity and broad applicability across bio
225 ere examined by using generalized estimating equations separately for CE spectral mammography and MR
226 ibution to derive acute and chronic criteria equations similar in form to the USEPA's current hardnes
227 etailed time-resolved mechanism, and kinetic equations solution for the ensemble long-time propagatio
228 ations, Monte Carlo simulations, and kinetic equations solution-as well as by structure-based binding
229 e subsequently developed and validated a GFR equation specifically for cirrhosis and compared the per
230                 While the standard Sellmeier equation (SSE) for atmospheric air is not intended for t
231 rium thermodynamics, combined with Maxwell's equations, suggest that colloidal particles heated or co
232                       Generalized estimating equations suggested that PERG amplitudes worsened more i
233 drug penetration by the 1D general diffusion equation that accounts for spatial variations in the dif
234 ing a 3-compartment model and an operational equation that included a k*4On 6 mornings, we completed
235  derived a novel form of the logistic growth equation that permits time-varying carrying capacity and
236 y functional theory based on spin projection equations that are exact within wave function theory.
237                  Using the resulting general equation, the Cu-O bond distance was predicted to be app
238                     For Partial Differential Equations, the crossing of infinity may persist for fini
239         Surprisingly, we also found a simple equation to describe the median frequency of transcript
240                            We develop a rate equation to describe the population dynamics within terr
241                 We finally provide a general equation to estimate the permeability of intact and frac
242  used the logistic equation and the Gompertz equation to fit the growth predictive model of Cladospor
243 exity measure is based on applying Shannon's equation to the number and diversity of paths up to two
244 istic regression with generalized estimating equations to account for clustering by site was used to
245 g-binomial regression and General Estimating Equations to account for correlation within clusters.
246 is was performed using generalized estimated equations to adjust for clustering of implants per parti
247 n consisting of individual plants to develop equations to predict heading date from marker genotypes.
248               We used generalised estimating equations to show predictors of LTC within 14 days and 3
249 aken into account when applying hydrodynamic equations to such deposits.
250 ommonly represented by a series of C balance equations to track C influxes into and effluxes out of i
251 onducted using maximum likelihood structural equation twin modeling.
252 using standard maximum likelihood structural equation twin modeling.
253                          Although the Tanaka equation using the evening specimen produced the least b
254 ing kinematics, solve the full Navier-Stokes equations using computational fluid dynamics with overse
255 studies to estimate coefficients of the risk equations using proportional hazard regressions.
256                                     The risk equation was generated as (1.27 x TBS) + (1.85 x lnAFP)
257 T above the threshold predicted by consensus equation was higher in the anaphylaxis group compared to
258 tion were developed, and the risk prediction equation was tested for its ability to discriminate pati
259                                Moreover, the equation was tested on literature data.
260                                          The equation was validated by measuring the 4 parameters by
261                      Thus, the corresponding equation was: Abs=4.00(+/-0.16) [tannic acid]+0.17(+/-0.
262 istic regression with generalized estimating equations was used to assess predictors of genital shedd
263            A system of ordinary differential equations was used to calculate protein turnover rates.
264     A biophysical equation (Augmented Growth Equation) was previously shown to accurately model the e
265 logy/American Heart Assocation pooled-cohort equations), we compared multivariable-adjusted hazard ra
266                             Using the Eyring equation, we established that their activation entropy f
267                          By fitting a growth equation, we estimated asymptotic growth, relative growt
268                  With generalized estimating equations, we analysed the effects of sex, age, puberty
269 Disease Epidemiology Collaboration (CKD-EPI) equations, we compared GFR estimated from creatinine (eG
270           To develop and validate these risk equations, we used data from the Action to Control Cardi
271  risk factors and to build a risk prediction equation were developed, and the risk prediction equatio
272                         Quadratic polynomial equations were developed to best fit the relationship be
273                                              Equations were developed with the use of the height-for-
274                                          The equations were solved numerically, and the solutions are
275                                        Gomez equations were used to estimate arteriolar afferent resi
276 gistic regression and generalized estimating equations were used to identify factors associated with
277    Linear models with generalized estimating equations were used to identify risk factors for BCVA lo
278 near mixed models and generalized estimating equations were used to model continuous and binary outco
279                       Generalized estimating equations were used to test the absolute least square me
280                               The analytical equations were validated through the simulation of the r
281 y spectrum agree with the basic ion mobility equation when using nitrogen as drift gas and also agree
282 ty of the lactulose (according to Van't Hoff equation), which was 98% and the melting point peak occu
283 22 different classes of partial differential equation, which can include Allee kinetics and nonlinear
284 using an ecological application of the Price equation, which partitions the contributions of richness
285 n of epsilon-values is based on the Rayleigh equation, which relates the change in measured isotope r
286                       The 2013 Pooled Cohort Equations, which predict composite rates of MI and strok
287  frequency) of the vector-field elastic wave equation with a given propagation constant.
288 near the threshold can be fitted by the Hill equation with a Hill coefficients of about -2.6 and 4.2,
289 as and also agree with a combination of this equation with Blanc's law when using purified air as dri
290                             We combined this equation with concepts drawn from disturbance ecology to
291 e traditionally described using an Arrhenius equation with energy barrier and pre-exponential factor
292 y of stochastic motion based on the Langevin equation with non-Wiener stochastic forcing that origina
293 thms can efficiently solve the Fokker-Planck equation with strongly non-Gaussian PDFs in much higher
294                       Thereby, we present an equation with two phenomenological parameters to predict
295  dilute photonic crystal, based on Maxwell's equations with a spatially dependent two dimensional inh
296 of CVD was estimated using the Pooled Cohort Equations with estimates >/=7.5% defining high CVD risk.
297 e to each gene frequently lead to systems of equations with many parameters whose behavior is obscure
298 icients are consistent and the classical PNP equations with renormalized coefficients are recovered,
299 onary game theory model using Lotka-Volterra equations with three competing cancer "species": androge
300 n produced the least bias overall, no single equation worked well across subgroups of sex and race/et

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