Abstract. The ability to detect the chaotic signal from a finite time series observation of hydrologic systems is addressed in this paper. The presence of random and seasonal components in hydrological time series, like rainfall or runoff, makes the detection process challenging.Tests with simulated data demonstrate the presence of thresholds, in terms of noise to chaotic-signal and seasonality to chaoticsignal ratios, beyond which the set of currently available tools is not able to detect the chaotic component. The investigations also indicate that the decomposition of a simulated time series into the corresponding random, seasonal and chaotic components is possible from finite data. Real streamflow data from the Arkansas and Colorado rivers are used to validate these results. Neither of the raw time series exhibits chaos. While a chaotic component can be extracted from the Arkansas data, such a component is either not present or can not be extracted from the Colorado data. This indicates that real hydrologic data may or may not have a detectable chaotic component. The strengths and limitations of the existing set of tools for the detection and modeling of chaos are also studied.
Let G = (V;E) be a graph. A total labeling ψ : V ⋃ E → {1, 2, ....k} is called totally irregular total k-labeling of G if every two distinct vertices u and v in V (G) satisfy wt(u) ≠wt(v); and every two distinct edges u1u2 and v1v2 in E(G) satisfy wt(u1u2) ≠ wt(v1v2); where wt(u) = ψ (u) + ∑uv∊E(G) ψ(uv) and wt(u1u2) = ψ(u1) + ψ(u1u2) + ψ(u2): The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G): In this paper, we determine the exact value of the total irregularity strength of cubic graphs.
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