represent in renewal theory the elapsed lifetimes of the "item in use" at time t. The limiting behavior of Y% as t—* °° has been extensively studied; if ju = £(X¿) < oo, Yt itself has a limiting distribution [8; 2] while if p= oo, the generalized arc-sine laws emerge as the possible limit distributions of Yt/t [2; 6]. It may be remarked that Yt forms a Markov process with right-continuous path ...

We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm equation is related to the KdV equation. In this paper we: (a) Derive a Lax pair. (b) Use the Lax pair to solve the initial value problem on the line. (c) Analyze s...

Results are obtained concerning the distribution of ranked relative lengths of excursions of a recurrent Markov process from a point in its state space whose inverse local time process is a stable subordinator. It is shown that for a large class of random times T the distribution of relative excursion lengths prior to T is the same as if T were a xed time. It follows that the generalized arc-si...

\7e have investigated the fluctuations of sums of random variables X.., Xp, ... . We have generalized previous results on the random variables H connected with this sequence, obtained new results on the validity of the Arc-sine Law for independent not identically distributed random variables, obtained a generalization of Spitzer's identity, and obtained a generalization of the equivalence princ...

This paper investigates and analyzes the dynamics of two-dimensional Duffing map. Multistability behavior has been observed from system numerically. Such behavior, especially coexistence chaotic periodic attractors, is undesirable in applications chaos-based cryptography. Therefore, we design implement a Sine–Cosine chaotification technique to enhance chaos multi-stable regions. Furthermore, th...

In this work, a microcontroller based circuit that performs the functions of an inverter /AVR hardware essentially consists of a PIC 16F877A microcontroller based circuit,. SG 3524 based modified sine-wave inverter driver circuit, a step-up. Modified sine wave inverter is designed to using pic microcontroller and push pull topology. output of control circuit for modified sine wave inverter The ...

In the presented research, uniqueness and existence of a mild solution for fractional system semilinear evolution equations with infinite delay an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative non-integer-order 1&lt;??2 parameter 0&lt;?&lt;1 used to establish our model. ?-Laplace transform strongly continuous cosine sine families uniformly bounde...