We consider the initial stage phase separation process in multi-component CahnHilliard systems through spinodal decomposition. Relying on recent work of MaierPaape and Wanner we establish the existence of certain dominating subspaces determining the behavior of most solutions originating near a spatially homogeneous state. It turns out that depending on the initial concentrations of the alloy c...

We regard a finite word u = u1u2 · · ·un up to word isomorphism as an equivalence relation on {1, 2, . . . , n} where i is equivalent to j if and only if ui = uj. Some finite words (in particular all binary words) are generated by palindromic relations of the form k ∼ j+i−k for some choice of 1 ≤ i ≤ j ≤ n and k ∈ {i, i+1, . . . , j}. That is to say, some finite words u are uniquely determined ...

A short proof is given for a result of Fraenkel and Simpson [Electronic J. Combinatorics 2 (1995), 159–164] stating that there exists an infinite binary word which has only three different squares u.

In this paper, we investigate the number of positions that do not start a square, the number of square occurrences, and the number of distinct squares in binary partial words. Letting σh(n) be the maximum number of positions not starting a square for binary partial words with h holes of length n, we show that limσh(n)/n = 15/31 provided the limit of h/n is zero. Letting γh(n) be the minimum num...

A word on a nite alphabet A is said to be overlap free if it contains no factor of the form xuxux where x is a letter and u a possibly empty word In this paper we study the number un of overlap free binary words of length n which is known to be bounded by a polynomial in n First we describe a bijection between the set of overlap free words and a rational language This yields recurrence relation...

Let w be an equality word of two nonperiodic binary morphisms g, h : {a, b}∗ → ∆∗. Suppose that no overflow occurs twice in w and that w contains at least 9 occurrences of a and at least 9 occurrences of b. Then either w = (ab)a, or w = ab with gcd(i, j) = 1, up to the exchange of letters a and b.

The force field describing the calculated interaction between atoms or molecules is key to accuracy of many molecular dynamics (MD) simulation results. Compared with traditional semi-empirical fields, machine learning fields have advantages faster speed and higher precision. We employed method atomic cluster expansion (ACE) combined first-principles density functional theory (DFT) calculations ...

The border correlation function β : A → A, for A = {a, b}, specifies which conjugates (cyclic shifts) of a given word w of length n are bordered, i.e., β(w) = b0b1 . . . bn−1, where bi = a or b according to whether the i-th cyclic shift σ(w) of w is unbordered or bordered. Except for some special cases, no binary word w has two consecutive unbordered conjugates (σ(w) and σ(w)). We show that thi...

abstract although flourishing research has been devoted to research on article abstracts, more studies are needed to unpack the relationship between rhetorical moves and their associated linguistic and rhetorical features (e.g., metadiscourse). to underpin this relationship, the current study analyzed a total of 60 research article abstracts written in english by two cultural groups in three di...