Some remarks on linear functional sequences

Some remarks on indiscernible sequences

We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of coheirs. Mathematics Subject Classification: 03C45

Some Remarks on Differentiable Sequences and Recursivity

We investigate the recursive structure of differentiable sequences over the alphabet {1, 2}. We derive a recursive formula for the (n + 1)-th symbol of a differentiable sequence, which yields to a new recursive formula for the Kolakoski sequence. Finally, we show that the sequence of absolute differences of consecutive symbols of a differentiable sequence u is a morphic image of the run-length ...

Remarks on some linear fractional stochastic equations

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...

Some Remarks on Linear Differential Systems*

Some remarks on signs in functional equations

To Robert Rankin Let k be a number field, and let M be a pure motive of weight n over k. Assume that there is a non-degenerate pairing M × M → Q(−n). For example, M could arise from the cohomology in degree n of a projective, smooth, geometrically connected variety X of dimension n over k, and the pairing from the cup product. In this case, the pairing will be symplectic (alternating) if n is o...