We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum P (k) ∝ k, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over previous simulations: we include a non-zero random background field in our box to simulate the effect of long-wavelength modes, and we examine the effects of smoothing ...

The coefficients of K. Goldberg in the infinite series for \o$(exey) for noncommuting x and y are computed as far as words of length twenty.

An infinite class of binary linear completely regular and completely transitive codes is given. The covering radius of these codes is growing with the length of the code.

Infinitely long rewrite sequences of possibly infinite terms are of interest for several reasons. Firstly, infinitary rewriting is a natural generalisation of finitary rewriting which extends it with the notion of computing towards a possibily infinite limit. Such limits naturally arise in the semantics of lazy functional languages, in which it is possible to write and compute with expressions ...

In this paper, we determine the maximum number of distinct Lyndon factors that a word of length n can contain. We also derive formulas for the expected total number of Lyndon factors in a word of length n on an alphabet of size σ, as well as the expected number of distinct Lyndon factors in such a word. The minimum number of distinct Lyndon factors in a word of length n is 1 and the minimum tot...

We revisit the notion of computational depth and sophistication for infinite sequences and study the density of the sets of deep and sophisticated infinite sequences. Koppel defined the sophistication of an object as the length of the shortest total program that given some data as input produces it and the sum of the size of the program with the size of the data is as consice as the smallest de...

In 2007 Jedwab and Parker proposed [10] that the natural viewpoint for a Golay complementary sequence is as a projection of a multi-dimensional Golay array. In 2008 Fiedler, Jedwab and Parker [5] used this viewpoint to show how to construct and enumerate all known 2-phase Golay sequences of length 2, starting from two sources of Golay seed pairs. The first source of seed pairs is the trivial Go...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

Entanglement between two qubits (two level atoms) mediated by surface plasmons in three-dimensional plasmonic waveguides is studied using a quantum master equation formalism. Two types of waveguides, a nanowire and a V-shaped channel cut in a flat metal plane, are considered. The Green functions for the waveguides, which rigorously describes the dissipative qubit environment, are calculated num...

The decorrelating and the linear, minimum mean-squared error (MMSE) detector for asynchronous code-division multiple-access communications ideally are infinite memory-length detectors. Finite memory approximations of these detectors require the inversion of a correlation matrix whose dimension is given by the product of the number of active users and the length of the processing window. With in...