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Equation linear

General first-order kinetics also play an important role for the so-called local eigenvalue analysis of more complicated reaction mechanisms, which are usually described by nonlinear systems of differential equations. Linearization leads to effective general first-order kinetics whose analysis reveals infomiation on the time scales of chemical reactions, species in steady states (quasi-stationarity), or partial equilibria (quasi-equilibrium) [M, and ]. [Pg.791]

Mixing mles for the parameters in an empirical equation of state, eg, a cubic equation, are necessarily empirical. With cubic equations, linear or quadratic expressions are normally used, and in equations 34—36, parameters b and 9 for mixtures are usually given by the following, where, as for the second virial coefficient, = 0-. [Pg.486]

From the Differential Equation Linear regression can be apphedwith the differential equation to obtain constants. Taking logarithms of Eq. (7-25),... [Pg.688]

First degree equations linear equations) have the form... [Pg.24]

The equations linearized about the steady state (with the apostrophes dropped from the deviation variables as in E4-38) are... [Pg.76]

Regression generally means the fitting of mathematical equations to experimental data ( 3). Nonlinear regression, unlike linear regression, encompasses methods vdiich are not limited to fitting equations linear in the coefficients (e.g. simple polynomial forms). [Pg.203]

The above equation is known as the linearized Poisson-Boltzmann equation since the assumption of low potentials made in reaching this result from Equation (29) has allowed us make the right-hand side of the equation linear in p. This assumption is also made in the Debye-Hiickel theory and prompts us to call this model the Debye-Hiickel approximation. Equation (33) has an explicit solution. Since potential is the quantity of special interest in Equation (33), let us evaluate the potential at 25°C for a monovalent ion that satisfies the condition e p = kBT ... [Pg.510]

Is the system of equations linear or nonlinear, and why Discuss also why the equations are coupled. [Pg.141]

Use the integrating factor method to find the general solutions to first-order differential equations linear in y... [Pg.136]

The only, but essential, use we make here of Eq. (11.19) is to extract the properties of the functions W u) etc. Note that by construction these functions are independent of (L, M), of momenta, and of chain lengths. Writing down Eq. (11.19) for three different choices of (L,M) we therefore have a system of three equations linear in W, 1/V, t/, which allows us to express these functions in terms of renormalized cumulants, Three important results immediately follow. [Pg.189]

Derivation van Vleck equation (linear magnetics) or expansion of Brillouin function Restrictions n Bg /kT < 1 - low fields and higher temperatures Formula Curie law Mean magnetic susceptibility... [Pg.63]

Derivation perturbation theory for eigenvalues (except S = 1, where the variation method is applied), van Vleck equation (linear magnetics)... [Pg.64]

All regression equations, linear by their regression coefficients, are analyzed by thus far developed methods. If an equation is not linear by coefficients we then deal with nonlinear regression equations, the analysis of which is very complicated and requires iterative procedures. [Pg.141]

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. [Pg.1]

For several cases, e.g. for linear pseudo-steady-state equations (linear mechanisms), the steady state is certain to be unique. But for non-linear mechanisms and kinetic models (which are quite common in catalysis, e.g. in the case of dissociative adsorption), there may be several solutions. Multiplicity of steady-states is associated with types of reaction mechanisms. [Pg.43]

When the B particles are present in great excess, the following integrodifferential equations linear in c describe the reversible contact reaction [47] ... [Pg.365]

Let us investigate the onset of steady bioelectric patterns. For these steady states dc/3t = 0, dv/dt = 0, and hence we must solve (56,57) with (6U) by setting 9c/dt = 0 in (57). Bifurcation theory shows that when a critical value of a parameter (such as a bath concentration) attains a critical value, small amplitude patterns arise from the uniform state ( V 1 here) in a pattern dictated usually by the equations linearized about the uniform state. The bifurcation condition for this patterning onset thus occurs when we can find solutions of... [Pg.192]

The result is always an equation linear in p with just one set of Pauli matrices <71 or [Pg.741]


See other pages where Equation linear is mentioned: [Pg.478]    [Pg.143]    [Pg.143]    [Pg.16]    [Pg.125]    [Pg.85]    [Pg.33]    [Pg.264]    [Pg.368]    [Pg.273]    [Pg.447]    [Pg.145]    [Pg.507]    [Pg.407]    [Pg.325]    [Pg.107]    [Pg.99]    [Pg.109]   
See also in sourсe #XX -- [ Pg.24 ]

See also in sourсe #XX -- [ Pg.74 ]




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Langevin equation linear response theory

Langevin equation, linear

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Non-linear equations

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Nonlinear phenomena linearized equations

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Numeric calculation linear equation system

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Second Order Linear Constant Coefficient Equation

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Simultaneous linear equations, solving

Solution Methods for Linear Finite Difference Equations

Solution of Linear Algebraic Equations

Solution of Linear Equation Systems

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Solving Linear and Nonlinear Equations

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