This paper continues our quest to develop a rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. The 18 yet uncharacterized local rules are henceforth partitioned into ten complex Bernoulli στ -shift rules and eight hyper Bernoulli στ -shift rules, the latter including such famous rules 30 and 110 . All exhibit a bizarre composite wave dynamics with arbitrar...

In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can estimate not only the main effects and pairwise interactions among the nodes b...

Arithmetic properties of integer sequences counting periodic points are studied, and applied to the case of linear recurrence sequences, Bernoulli numerators, and Bernoulli denominators.

This paper features the modeling and design of a Fast Output Sampling (FOS) Feedback control technique for the Active Vibration Control (AVC) of a smart flexible aluminium cantilever beam for a Single Input Single Output (SISO) case. Controllers are designed for the beam by bonding patches of piezoelectric layer as sensor / actuator to the master structure at different locations along the lengt...

in this paper, the modified euler-bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. an explicit solution is derived for the buckling loads of microscaled euler beams considering surface effects. the size-dependent buckling behavior of the nanotube d...

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli is allowed upon the arrival both primary (from outside) and customers orbit), as well that may occur after each service in system. Servers can break down during when they idle. If a server breaks customer, then interrupted accordance scheme, decides either to leave system or join co...

This paper examines the fault-tolerant control problem for discrete-time descriptor systems that are susceptible to intermittent actuator failures, nonlinear sensor data, and probability-based missing data. The non-homogeneous Markov chain was adopted describe stochastic behavior of faults. Moreover, Bernoulli-distributed variables with known conditional probabilities were employed practical fe...