Recurrence relations particles

The physical state of a system with a varying number of particles is defined uniquely by a set of the population numbers j (f i),..., a(r ) = i/(f ) jv-Assuming the reaction is the Markov process, let us introduce the distribution functions (DF s) P( i/(r ) yv t) yielding a complete probabilistic description of the problem. The recurrent relation... 

In the case of isotropic magnetic particles, that is, TJ = -p(e H), both linear and cubic dynamic susceptibilities may be obtained analytically. To show this, we first transform Eq. (4.90) into an infinite set of differential recurrence relations ... 

The propagator [/ of a spin-1/2 particle, propagating from right to left through M, satisfies the recurrence relation... 

A general calculation of the average number of radicals per particle in these systems is complicated by the fact that a probabilistic analysis leads to a third-order recurrence relation due to the p -wise generation of radicals in the... 

This formalism will be used in Sect. 2.5 to derive a recurrence relation for the transition matrix of a multilayered particle. 

The corresponding recurrence relation for increments in the second index is identical except that XpA is replaced by XpB. The recurrence relation for increments in the third index is obtained from (9.11.62) by interchange of the quantities that refer to particles 1 and 2 ... 

In conclusion, most of the recurrent difficulties can be identified in terms of the contexts in which concepts and procedures are used. Various conceptual difficulties are caused by the prominent impact of the physics particulate context, for instance, students conception that the current flow in the electrolyte corresponds to the transport of electrons. When students try to explain electrochemical cell phenomena, it appeared to be very difficult for them to relate a physics context (transport of particles) to a chemical context (transfer of electrons and ions). 

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