We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.

the understanding of the dynamic behavior of distillation columns has received considerable attention because distillation is one of the most widely used unit operations in chemical process industries. this paper reports a dynamic simulation study of the possible distillation columns sequences of dew pointing unit in the second phase of south pars gas refinery. in this unit, three columns are u...

Given an i.i.d. sequence of n letters from a finite alphabet, we consider the length of the longest run of any letter. In the equiprobable case, results for this run turn out to be closely related to the well-known results for the longest run of a given letter. For coin-tossing, tail probabilities are compared for both kinds of runs via Poisson approximation.

In this paper, rstly we have introduced to entropy of sequences of fuzzy sets and given sometheorems about it. Secondly, the waves P and T which appears in electrocardiograms weretransferred to fuzzy sets, by using denition of entropy for sequences of fuzzy sets, and somenumerical values were obtained for sequences of waves P and T. Thus any person can makea medical predictions for some cardiac...