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Linearized model

The analyst now has available the complete details of the chemical composition of a gasoline all components are identified and quantified. From these analyses, the sample s physical properties can be calculated by using linear or non-linear models density, vapor pressure, calorific value, octane numbers, carbon and hydrogen content. [Pg.73]

From these data, a first approach is to develop linear models using a relation of the following type ... [Pg.205]

To predict the octane numbers of more complex mixtures, non-linear models are necessary the behavior of a component i in these mixtures depends on its hydrocarbon environment. [Pg.205]

We present in this paper an eddy current imaging system able to give an image of three-dimensional flaws. We implement a multifrequency linearized model for solving the 2590... [Pg.332]

The LIN method (described below) was constructed on the premise of filtering out the high-frequency motion by NM analysis and using a large-timestep implicit method to resolve the remaining motion components. This technique turned out to work when properly implemented for up to moderate timesteps (e.g., 15 Is) [73] (each timestep interval is associated with a new linearization model). However, the CPU gain for biomolecules is modest even when substantial work is expanded on sparse matrix techniques, adaptive timestep selection, and fast minimization [73]. Still, LIN can be considered a true long-timestep method. [Pg.245]

The skeletal LN procedure is a dual timestep scheme, At, Atm, of two practical tasks (a) constructing the Hessian H in system (17) every Atm interval, and (b) solving system (17), where R is given by eq. (3), at the timestep At by procedure (23) outlined for LIN above. When a force-splitting procedure is also applied to LN, a value At > Atm is used to update the slow forces less often than the linearized model. A suitable frequency for the linearization is 1-3 fs (the smaller value is used for water systems), and the appropriate inner timestep is 0.5 fs, as in LIN. This inner timestep parallels the update frequency of the fast motions in force splitting approaches, and the linearization frequency Atm) is analogous to the medium timestep used in such three-class schemes (see below). [Pg.251]

An instability of the impulse MTS method for At slightly less than half the period of a normal mode is confirmed by an analytical study of a linear model problem [7]. For another analysis, see [2]. A special case of this model problem, which gives a more transparent description of the phenomenon, is as follows Consider a two-degree-of-freedom system with Hamiltonian p + 5P2 + + 4( 2 This models a system of two springs con-... [Pg.324]

To see how cahbration can be extended to multicomponent analysis, the linear model of equation 10 can be generalized to accommodate several analytes in the same sample, and several measurements made on each sample. Expressed in matrix notation, this becomes... [Pg.427]

McIntosh, A. Fitting Linear Models An Application of Conjugate Gradient Algorithms, Springer-Verlag, New York (1982). [Pg.423]

Multiple Regression A general linear model is one expressed as... [Pg.502]

Nonlinear versus Linear Models If F, and k are constant, then Eq. (8-1) is an example of a linear differential equation model. In a linear equation, the output and input variables and their derivatives only appear to the first power. If the rate of reac tion were second order, then the resiilting dynamic mass balance woiild be ... [Pg.720]

A key featui-e of MPC is that a dynamic model of the pi ocess is used to pi-edict futui e values of the contmlled outputs. Thei-e is considei--able flexibihty concei-ning the choice of the dynamic model. Fof example, a physical model based on fifst principles (e.g., mass and energy balances) or an empirical model coiild be selected. Also, the empirical model could be a linear model (e.g., transfer function, step response model, or state space model) or a nonhnear model (e.g., neural net model). However, most industrial applications of MPC have relied on linear empirical models, which may include simple nonlinear transformations of process variables. [Pg.740]

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... [Pg.140]

Equation 3-241 is a linear model of the form Y = Co + CiXi + C2X2... [Pg.175]

The number of cancers over the next 70 years firom this exposure, was estimated using the conservative linear model to be 160 which should be compared with 27,000 cancers the evacuees will get from natural causes over 70 years. Thus, the long-term effect of the accident will be... [Pg.227]

Once the indicator is defined, a model can be developed that predicts the indicator value as a function of an emission. Such models are normally simple linear models defined by characterization factors. If an emission is niuitiplied by a characterization factor, an indicator value is obtained. [Pg.1363]

The vibrations of the diaeetylenie grouping in pyrazole 96 split into symmetrie and antisymmetrie modes. In this ease, aeeording to the linear model of two oseil-lators with an elastie bond, the former must have a higher frequeney owing to the rigidity of the Ci=C2 bond. [Pg.71]

Fig. E.2.2. Linear model for the Monod rate equation with populated data at the origin. Fig. E.2.2. Linear model for the Monod rate equation with populated data at the origin.
Adsorption, like extraction, depends on equilibrium relationships. Isothermal adsorption is projected by Langmuir isotherms. The model is shown in Figure 7.14, which is based on the linear model of the following equation ... [Pg.186]

Figure 15.4 shows the linear model for (15.6.3), the loss of cell viability at various temperatures. As the temperature increases from 105 to 121 °C, the value for the slope of the line increases. This means that the number of viable cells at a fixed time of sterilisation will drastically decrease as the temperature increases by 16 °C. [Pg.347]

Fig. 4 Predicted versus observed summer Anoxic Factor (AF) in (a, b) Foix Reservoir (Spain), (c, d) San Reservoir (Spain), (e, f) Brownlee Reservoir (USA), and (g, h) Pueblo Reservoir (USA). The results have been arranged to place the systems along a gradient of relative human impact (Foix Reservoir at the top, Pueblo Reservoir at the bottom). Predictions are based on linear models using different independent variables (in brackets) Inflow = streamflow entering the reservoir during the period DOCjjiflow = mean summer river DOC concentration measured upstream the reservoir CljjjAow = mean summer river CU concentration measured upstream the reservoir and Chlepi = mean summer chlorophyll-a concentration measured in the epilimnion of the reservoir. The symbol after a variable denotes a nonsignificant effect at the 95% level. Solid lines represent the perfect fit, and were added for reference. Modified from Marce et al. [48]... Fig. 4 Predicted versus observed summer Anoxic Factor (AF) in (a, b) Foix Reservoir (Spain), (c, d) San Reservoir (Spain), (e, f) Brownlee Reservoir (USA), and (g, h) Pueblo Reservoir (USA). The results have been arranged to place the systems along a gradient of relative human impact (Foix Reservoir at the top, Pueblo Reservoir at the bottom). Predictions are based on linear models using different independent variables (in brackets) Inflow = streamflow entering the reservoir during the period DOCjjiflow = mean summer river DOC concentration measured upstream the reservoir CljjjAow = mean summer river CU concentration measured upstream the reservoir and Chlepi = mean summer chlorophyll-a concentration measured in the epilimnion of the reservoir. The symbol after a variable denotes a nonsignificant effect at the 95% level. Solid lines represent the perfect fit, and were added for reference. Modified from Marce et al. [48]...
Thus, Tis a linear function of the new independent variables, X, X2,. Linear regression analysis is used to ht linear models to experimental data. The case of three independent variables will be used for illustrative purposes, although there can be any number of independent variables provided the model remains linear. The dependent variable Y can be directly measured or it can be a mathematical transformation of a directly measured variable. If transformed variables are used, the htting procedure minimizes the sum-of-squares for the differences... [Pg.255]

Thus, the linear model is undoubtedly the most important one in the treatment of two-dimensional data and will therefore be discussed in detail. [Pg.95]


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See also in sourсe #XX -- [ Pg.171 , Pg.172 , Pg.173 , Pg.174 , Pg.175 , Pg.176 , Pg.177 , Pg.178 , Pg.179 , Pg.180 , Pg.181 , Pg.182 , Pg.183 , Pg.184 , Pg.185 , Pg.186 ]

See also in sourсe #XX -- [ Pg.20 ]




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A General Theorem for Simple, Linear Reactor Models

Accounting linear program models

Adaptations of linear theory - differential models

Adaptations of linear theory - integral models

Adequate linear model

Advance Catalyst Evaluation unit best linear regression model

Alternative Linear Regression Models

Analysis of Variance (ANOVA) for Linear Models

Angular distributions rotating linear model

Another method to obtain canonical models with linear terms

Antigen retrieval linear epitope model

Approximate confidence levels and regions for non-linear models

Atomic orbitals linear combination model

Basis functions linear models

Bending corrected rotating linear model BCRLM)

Bending-corrected rotating linear model

Calibration model linear

Case studies of QSPRs obtained by linear modeling

Computing Optimal Weights by Linear Programming Model

Correlation between parameters for non-linear models

Disease progress models linear

Dispersive Linear Chain model

Dose-Response Models linear

Dose-Response Models linear quadratic

Dose-response assessment linearized-multistage model

Dynamic linear modeling

Dynamic system linear modeling

Empirical (linear) Dynamic Models

Engineering problems linear models

Experimental models linear model

Extension of Linear to Nonlinear Chromatography Models

Factorial design linear models

First-order absorption models linear regression

Fractional linear solid model

Freundlich model linear form

Full linear model, with

Full linear model, with adsorption-desorption

General linear model

General linear model approach

Generalized linear Maxwell model

Generalized linear model

Generalized linear viscoelastic model

Generation of Linear Models in Standard Forms

Gradient elution linear solvent strength model

Gradient linear model

Group contribution models linear

HF-LCAO (Hartree Fock Linear model

Inadequate linear model

Intrinsically linear models

KS-LCAO (Kohn-Sham Linear Model

Kinetic Modeling of Linear Reversible Polycondensations

Kinetic model linear

Kinetic modeling linear logarithmic kinetics

Langmuir model linear form

Linear Combinations of Model Compounds

Linear Compartmental Models

Linear Coupled Cluster Doubles model

Linear Driving Force Model Approach

Linear Isotherm Systems—Solution to the General Model

Linear Isotherm System—Simple Models

Linear Model Creation and Validation

Linear Programming Model for Aggregate Planning

Linear QSAR models

Linear QSAR models descriptor pharmacophores

Linear Solvent Strength model

Linear Three-Element Models

Linear adsorption isotherm, assumption model

Linear airflow models

Linear alternative models

Linear behavior model

Linear cascade model

Linear chain model

Linear chromatography statistical model

Linear combination of atomic orbitals LCAO model)

Linear continuum model

Linear coupling model

Linear coupling model, vibrational contributions

Linear curve crossing model

Linear discrete model

Linear driving force model

Linear driving force model, for mass transfer

Linear elastic dumbbell model

Linear elastic material model

Linear epitope model of antigen

Linear free energy relation models

Linear free-energy related model

Linear least-squares regression model

Linear life-cycle model

Linear logistic regression model

Linear mass bias model

Linear mixed effects model

Linear mixed effects model general

Linear model

Linear model with intercept

Linear model, risk calculation

Linear modeling

Linear modeling by best subset selection

Linear modeling by stepwise subset selection

Linear modeling using principal component regression

Linear modeling using substructure counts

Linear modeling using topological indices

Linear models average speed

Linear models characteristics

Linear models dependent variables

Linear models independent variables

Linear models quantity

Linear models resistivity values

Linear models scalar quantity

Linear models vector

Linear models, confidence intervals

Linear molecules VSEPR model

Linear multivariable models

Linear multivariate model

Linear no-threshold model

Linear partitioning model

Linear partitioning sorption model

Linear process model

Linear process model state-space representation

Linear process model variable scaling

Linear programming minimal models

Linear programming modeling systems

Linear programming models

Linear programming, process modeling

Linear programming, process modeling using

Linear reactor models

Linear reduced model

Linear regression models

Linear response , excited state model

Linear response approximation models

Linear response phonon model

Linear response theory mechanics model

Linear solvation energy relationship model

Linear solvent strength gradient model

Linear stochastic model formulations

Linear system graph model

Linear system membrane transport model

Linear systems models

Linear vibronic-coupling model

Linear viscoelastic model Maxwell

Linear viscoelastic model, description

Linear viscoelastic models

Linear viscoelastic models dynamic moduli

Linear viscoelastic solids three-parameter model

Linear viscoelasticity four-parameter model

Linear viscoelasticity mechanical models

Linear viscoelasticity) Kelvin-Voigt model

Linear viscoelasticity) Maxwell model

Linear-eddy model

Linear-quadratic model

Linear-response model

Linear-transfer model

Linearization of Model Equations

Linearization of non-linear models

Linearization of the Chemical Reactor Model

Linearized Multistage model

Linearized model accurate near steady state

Linearized model, dimensionality

Linearized multistage model, estimation

Linearized theory film model

Linearized theory penetration model

Linearizing models

Linearly elastic dumbbell model

Log-linear model

Log-linear modeling

Mass transfer linear driving force model

Material modeling linear elasticity

Material modeling linear viscoelasticity

Mathematical models linear programming

Matrix models linear difference equations

Maximum likelihood estimation linear model

Maxwell model Linear

Maxwell model linear viscoelastic behaviour

Mechanical models for linear viscoelastic

Mechanical models for linear viscoelastic response

Mechanical models standard linear solid

Mechanistic Non-linear Models

Mixed linear models

Model Analogies of Linear Viscoelastic Behavior

Model Linearity

Model Linearity

Model linear probabilistic

Model solid film linear driving force

Model systems linear additive models

Model, linear dynamic

Modeling Linear Free Energy Relationship

Modeling of Response in Linear Systems

Modeling, linear control system

Models linear discrete-time transfer

Models linear elastic dumbbell model

Models linear model

Models linear model

Models linear rollback

Models linearization

Models linearization

Models of linear chromatography

Molecular mixing models linearity

Multidimensional model linear

Multiple linear regression calibration model

Multiple linear regression inverse least squares model

Multiple linear regression model

Multiple linear regression model prediction

Multiple linear regression. Least squares fitting of response surface models

Multiscale denoising with linear steady-state models

Multivariate linear regression models

Non-linear Mathematical Model

Non-linear Process Modeling

Non-linear Process Models

Non-linear model

Non-linear viscoelastic models

Nonlinear versus Linear Models

Normal linear regression model

Observations from Normal Linear Regression Model

Optimization for Models Linear in the Parameters

Optimization linear models

Oscillation Model linear density

Other Linear Response and LIE Models

Parameter estimation linear model, single reaction

Pharmacodynamics linear models

Point Charge Model of XY2 Linear Symmetric Molecules

Polarizable Continuum Model linear-response

Prediction and Extrapolation in the Simple Linear Model

Process control linear models

Process modeling using linear programming program models

Quantitative structure-activity linear models

Reactive resonances rotating linear model

Rotating linear model

Shell Model of the Linear Monoatomic Chain

Simple Linear Trend Model

Simple linear model analysis

Simple linear regression model

Simplest Linear Model

Simulation of Linear and Nonlinear Models

Solving the Model Using Linear Programming

Stability linear model

Standard linear solid model

State-space models linear

Statistical models linear regression

The General Linear Mixed Effects Model

The Linear Model

The Linear Model for Conical Intersection

The Linear Regression Model

The Multiple Linear Regression Model

The Standard Linear Model

Tube Models for Linear Polymers - Advanced Topics

Tube Models for Linear Polymers - Fundamentals

Two Models of Linear Mass Transport

Univariate linear model

Univariate linear regression model)

VSEPR model linear structures

Viscoelastic models standard linear solid

Viscoelasticity linear viscoelastic model

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