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Models linearization

The implicit-midpoint (IM) scheme differs from IE above in that it is symmetric and symplectic. It is also special in the sense that the transformation matrix for the model linear problem is unitary, partitioning kinetic and potential-energy components identically. Like IE, IM is also A-stable. IM is (herefore a more reasonable candidate for integration of conservative systems, and several researchers have explored such applications [58, 59, 60, 61]. [Pg.241]

Linear paraffins Linear programming Linear rollback model Linear sensor arrays Linear superelasticity Linear topology Linear units Linen... [Pg.568]

Simulation of Dynamic Models Linear dynamic models are particularly useful for analyzing control-system behavior. The insight gained through linear analysis is invaluable. However, accurate dynamic process models can involve large sets of nonlinear equations. Analytical solution of these models is not possible. Thus, in these cases, one must turn to simulation approaches to study process dynamics and the effect of process control. Equation (8-3) will be used to illustrate the simulation of nonhnear processes. If dcjdi on the left-hand side of Eq. (8-3) is replaced with its finite difference approximation, one gets ... [Pg.720]

The first is the relational model. Examples are hnear (i.e., models linear in the parameters and neural network models). The model output is related to the input and specifications using empirical relations bearing no physical relation to the actual chemical process. These models give trends in the output as the input and specifications change. Actual unit performance and model predictions may not be very close. Relational models are usebil as interpolating tools. [Pg.2555]

The formulation of the parameter estimation problem is equally important to the actual solution of the problem (i.e., the determination of the unknown parameters). In the formulation of the parameter estimation problem we must answer two questions (a) what type of mathematical model do we have and (b) what type of objective function should we minimize In this chapter we address both these questions. Although the primary focus of this book is the treatment of mathematical models that are nonlinear with respect to the parameters nonlinear regression) consideration to linear models linear regression) will also be given. [Pg.7]

Computation of Parameters in Linear Models - Linear Regression... [Pg.23]

Figure 1 Stress relaxation of a Maxwell model (linear scales), T = 1 s. Figure 1 Stress relaxation of a Maxwell model (linear scales), T = 1 s.
The linear bond in 12 Br4 is analyzed by the 6c 8e model. Linear Br-Se-Br 3c-4e bonds in 1 Br2 interact mutually to give 12 Br4, which contains the linear alignment of the six Se2Br4 atoms. The linear bond in 12 Br6 is analyzed... [Pg.661]

Three kinetic models were applied to adsorption kinetic data in order to investigate the behavior of adsorption process of adsorbates catechol and resorcinol onto ACC. These models are the pseudo-first-order, the pseudo-second-order and the intraparticle diffusion models. Linear form of pseudo-first-order model can be formulated as... [Pg.218]

Model Fitting When experimental variograms reveal the structure and distribution pattern in an ore body then for any further estimation, it is necessary to fit a mathematical model to experimental variograms, which are called theoretical variograms. These mathematical models will be used in Kriging estimation. Several predefined models (Linear, Spherical, Gaussian, etc.). [Pg.400]

Traditional regression-type models have been linear and quadratic regression models. Linear and quadratic regression models unfortunately impose further constraints upon the nature of the process nonlinearity as such, these models are limited in the range of their applicability. A relatively new nonlinear regression-type model—the Artificial Neural Network (ANN)—is not as limited, and is worthy of additional discussion. [Pg.284]


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See also in sourсe #XX -- [ Pg.65 ]




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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

Linearized 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 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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