We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of ${\mathbb {R}}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for ionic concentrations. prove existence smooth steady state solutions and present sufficient condition terms only data that guarantees these have nonzero fluid velocity. show time evolving are ultimately uniformly, independently their i...

Quantitative experiments are described on spatio-temporal patterns of coherent chemical signaling activity in populations of Dictyostelium discoideum amoebae. We observe competition between spontaneously firing centers and rotating spiral waves that depends strongly on the overall cell density. At low densities, no complete spirals appear and chemotactic aggregation is driven by periodic concen...

One can study variations of this discrete dynamical system : applying the rule sequentially (on exactly one vertex at each time step), the restriction to undirected graphs or other families of graphs, the extension to multi-graphs, etc. Such models are called chip-firing games (CFG). Some original definitions where given in [19] and [1], but the two references to this respect are [4] for the un...

Self-healing of the superhydrophobic cotton fabric (SCF) obtained by the radiation-induced graft polymerization of lauryl methacrylate (LMA) and n-hexyl methacrylate (HMA), can be achieved by ironing. Through the steam ironing process, the superhydrophobicity of the SCFs will be regenerated even after the yarns are ruptured during the abrasion test under a load pressure of 44.8 kPa. SCFs made f...

Suppose f : X∗ −→ X∗ is a morphism and u, v ∈ X∗. For every nonnegative integer n, let zn be the longest common prefix of f(u) and f(v), and let un, vn ∈ X∗ be words such that f(u) = znun and f(v) = znvn. We prove that there is a positive integer q such that for any positive integer p, the prefixes of un (resp. vn) of length p form an ultimately periodic sequence having period q. Further, there...

We study the Shallit's conjecture which states that an in nite word ! is ultimately periodic if and only if lim n!1 inf jun(!)j n > 3 p5 2 ; where un(!) is the longest su x of length n pre x of ! which occurs also inside length n 1 pre x of !. We prove that a weaker condition holds, namely that the conjecture is true if the constant 3 p5 2 is replaced by 13 p69 10 . TUCS Research Group Mathemat...

We introduce and study a new complexity function on words, that we call cyclic complexity, which counts the number of conjugacy classes of factors of each given length. We extend the famous MorseHedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity dis...

Evidence suggests that most hyperthyroid patients have a proximal myopathy. The more severe this is the more frequently are distal muscles, and ultimately, bulbar muscles involved. Probably acute thyrotoxic myopathy or encephalopathy supervenes on a previous chronic background or occurs concurrently with skeletal muscle involvement. Using careful electromyographic techniques evidence of myopath...

We examine the Sprague-Grundy values of F-Wythoff, a restriction of Wythoff’s game introduced by Ho, where the integer ratio of the pile sizes must be preserved if the same number of tokens is removed from both piles. We answer two conjectures raised by Ho. First, we show that each column of Sprague-Grundy values is ultimately additively periodic. Second, we prove that every diagonal of Sprague...

Neutrophils undergo periodic cytoskeletal rearrangements that lead to cycles of shape change, ultimately resulting in cell translocation. Repeated stimulation of resting neutrophils with subsaturating chemoattractant doses induced transient sinusoidal oscillations in neutrophil filamentous actin content at the second and subsequent stimulations. Oscillation frequencies increased with increasing...