We give a general construction for the classical limit of a quantum system defined in terms of generators of an arbitrary compact semisimple Lie algebra, generalizing known results for the su2 and su3 cases. The classical limit depends on the physical problem in question and is determined by the sequence of representations by which it is reached. Only in the simplest cases it is unique. We pres...

In many real systems in which a state variable should be controlled for being in appropriate range, the length of control (review) intervals is taken to be constant. In such systems, when the cost of reviews and out-of-range values of the state variable are considerable, this method may not be optimal. In this paper we let the length of review intervals to be variable during each operating cycl...

Now we recall the statement of the central limit theorem (CLT) and give a proof in the case of IID (independent identically distributed) random variables. The weak law of large numbers says that if Xn is a sequence of IID random variables with E[Xn] = 0, then writing Sn = ∑n−1 k=0 Xk, the time averages 1 n Sn converge to 0 in probability, or equivalently (since the limit is a constant), in dist...

limit to the tension reinforcement ratio ( ρ) in flexural high strength reinforced concrete (hsrc) members is based on the requirement that tension failure as sufficient rotation capacity are ensured at ultimate limit state. however, the provisions for the total amount of longitudinal reinforcement ratio ( ρ and ρ’) are not associated with any rational derivation. in this paper, a quantitative ...

We represent a filamentous actin molecule as a graph of finite-state machines (F-actin automaton). Each node in the graph takes three states — resting, excited, refractory. All nodes update their states simultaneously and by the same rule, in discrete time steps. Two rules are considered: threshold rule — a resting node is excited if it has at least one excited neighbour and narrow excitation i...