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  2. Exponential stability - Wikipedia

    en.wikipedia.org/wiki/Exponential_stability

    The impulse responses of two exponentially stable systems. The graph on the right shows the impulse response of two similar systems. The green curve is the response of the system with impulse response () =, while the blue represents the system () = ⁡ ().

  3. Lyapunov stability - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_stability

    The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations.

  4. Chemical stability - Wikipedia

    en.wikipedia.org/wiki/Chemical_stability

    In chemistry, chemical stability is the thermodynamic stability of a chemical system, in particular a chemical compound or a polymer. [ 1 ] Thermodynamic stability occurs when a system is in its lowest energy state , or in chemical equilibrium with its environment.

  5. Linear stability - Wikipedia

    en.wikipedia.org/wiki/Linear_stability

    In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form / =, where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part.

  6. Thermodynamic activity - Wikipedia

    en.wikipedia.org/wiki/Thermodynamic_activity

    The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.

  7. Determination of equilibrium constants - Wikipedia

    en.wikipedia.org/wiki/Determination_of...

    When determining the stability constants for ternary complexes, M p A q B r it is common practice the fix the values for the corresponding binary complexes M p′ A q′ and M p′′ B q′′, at values which have been determined in separate experiments. Use of such constraints reduces the number of parameters to be determined, but may result ...

  8. Transition state theory - Wikipedia

    en.wikipedia.org/wiki/Transition_state_theory

    In chemistry, transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes. [1] TST is used primarily to understand qualitatively how chemical reactions take place.

  9. Magic number (chemistry) - Wikipedia

    en.wikipedia.org/wiki/Magic_number_(chemistry)

    The concept of magic numbers in the field of chemistry refers to a specific property (such as stability) for only certain representatives among a distribution of structures. It was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. [ 1 ]

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