Linear Recurring Sequences with Cycle Shift Operator over F_4
This paper presents a new_type linear recurring sequence model over F_4 by adding cycle shift operator to linear recurring sequence over F_4. We first transform study of the model into research on linear recurring sequence over a module. With the aid of matrix representation, we turn it into further study on properties of polynomial matrix of rank 2 over F_2. Nonsingularity of this new linear recurring sequence is discussed in the end.
We present what is to our knowledge the most complete 1-D numerical analysis of the evolution and the propagation ::: dynamics of an ultrashort laser pulse in a Ti:Sapphire laser oscillator. This study confirms the dispersion ::: managed model of mode-locking, and emphasizes the role of the Kerr nonlinearity in generating mode-locked ::: spectra with a smooth and well-behaved spectral phase. A very good agreement with experimental measurements ::: of pulse energy, spectrum, and temporal width of extracavity compressed pulses is found.