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In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...
The ethoxy and cyano groups are able to delocalize the radical ion in the transition state, thus stabilizing the radical center. The rate enhancement is due to the captodative effect. When R = H, the reaction has the largest energy of activation because the radical center is not stabilized by the captodative effect.
For higher degree polynomials the extra computation involved in this mapping can be avoided by testing the Schur stability by the Schur-Cohn test, the Jury test or the Bistritz test. Necessary condition: a Hurwitz stable polynomial (with real coefficients) has coefficients of the same sign (either all positive or all negative).
The phosphinyl radicals synthesised by Lappert and co-workers were found to be stable at room temperature for periods of over 15 days with no effect from short-term heating at 360 K. [4] This stability was assigned to the steric bulk of the substituents and the absence of beta-hydrogen atoms.
As a stable and well-characterized solid radical source, DPPH is the traditional and perhaps the most popular standard of the position (g-marker) and intensity of electron paramagnetic resonance (EPR) signals – the number of radicals for a freshly prepared sample can be determined by weighing and the EPR splitting factor for DPPH is calibrated at g = 2.0036.
Bent's rule predicts that, in order to stabilize the unshared, closely held nonbonding electrons, lone pair orbitals should take on high s character. On the other hand, an unoccupied (empty) nonbonding orbital can be thought of as the limiting case of an electronegative substituent, with electron density completely polarized towards the ligand ...
The Z group primarily affects the stability of the S=C bond and the stability of the adduct radical (Polymer-S-C•(Z)-S-Polymer, see section on Mechanism). These in turn affect the position of and rates of the elementary reactions in the pre- and main-equilibrium.
Radical polymerisation of unsaturated monomers is generally propagated by C-radicals. These can be effectively terminated by combining with other radicals to form neutral species and many true inhibitors operate through this mechanism. In the simplest example oxygen can be used as it exists naturally in its triplet state (i.e. it is a diradical).