We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies longest subsequence which occurs twice without overlap in This is based on Hunt-Szymanski algorithm, therefore its performance improves if string not self similar, naturally strings over large alphabets. relies new results for data structures that support dynamic increasing sub-sequenc...

We study the class of first-countable Lindel\"of scattered spaces, or "FLS" spaces. While every $T_3$ FLS space is homeomorphic to a subspace $\mathbb Q$, $T_2$ spaces turns out be surprisingly rich. Our investigation these reveals close ties $Q$-sets, Lusin sets, and their relatives, cardinals $\mathfrak{b}$ $\mathfrak{d}$. Many natural questions about turn independent $\mathsf{ZFC}$. prove th...

Sequences of characters called words or strings are widely studied in combinatorics, and used in various fields of sciences (e.g. chemistry, physics, social sciences, biology [2, 3, 4, 11] etc.). The elements of a word are called letters. A contiguous part of a word (obtained by erasing a prefix or/and a suffix) is a subword or factor. If we erase arbitrary letters from a word, what is obtained...

An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Moreover, using...

Fluctuations in scattered light constitute some of the most familiar natural optical phenomena, including the twinkling of starlight, the glittering of sunlight on a rippled water surface and the shimmering of distant objects on a hot day [1]. These effects are geometrical in origin being a consequence of refraction by large-scale random variations in refractive index. Fluctuations of this kind...