In this paper we consider analytically and numerically the dynamics of waves in twodimensional, magnetically trapped Bose-Einstein condensates in the weak interaction limit. In particular, we consider the existence and stability of azimuthally modulated structures such as rings, multi-poles, soliton necklaces, and vortex necklaces. We show how such structures can be constructed from the linear ...

Cosmic strings in the brane Universe have recently gained a great interest. I think the most interesting story is that future cosmological observations distinguish them from the conventional cosmic strings. If the strings are the higher-dimensional objects that can (at least initially) move along the compactified space, and finally settle down to (quasi-)degenerated vacua in the compactified sp...

A flip-swap language is a set \(\mathbf{S}\) of binary strings length n such that \(\mathbf{S} \cup \{0^n\}\) closed under two operations (when applicable): (1) Flip the leftmost 1; and (2) Swap 1 with bit to its right. Flip-swap languages model many combinatorial objects including necklaces, Lyndon words, prefix normal left factors k-ary Dyck feasible solutions 0-1 knapsack problems. We prove ...