We prove that every topologically transitive map f on the real line must satisfy the following properties:(1) The set C of critical points is unbounded.(2) The set f (C) of critical values is also unbounded.(3) Apart from the empty set and the whole set, there can be at most one open invariant set.(4) With a single possible exception, for every element x the backward orbit {y ∈ R : f n (y) = x for some n in N} is dense in R.
We present a rare case in which a young girl ingested a solution of a hair-removing soap. The ingestion resulted in profound hypokalemia and severe acidosis leading to flaccid paralysis, respiratory arrest and ventricular arrhythmias. Ultimately the patient made complete recovery. The soapwas found to contain barium sulfide. The degree of paralysis and acidosis appeared to be directly related to serum potassium levels.
The introduction of unsupervised learning techniques like K-means inside the domain of Image Processing plays a vital role in Image Segmentation. The hybridization of this Algorithm by using Swarm Intelligent techniques further more improves the efficiency. Various works on hybridization of Particle Swarm Optimization (PSO) with K-means have been proposed and are found to be efficient in Image Segmentation. However, the PSO has a problem of getting stagnated with the local optima. This results in the degradation of the Image Segmentation process in most cases. The main reason behind this problem is the constancy of the inertia weight. The inertia weight when varied dynamically and exponentially could afford a better performance in the process of finding better global optima. We use the Exponential Particle Swarm Optimization to enhance the K-means Algorithm. This shows a drastic improvement in the process of Image Segmentation. The experimental results obtained also add to this process enhancement. The EPSO K-means Algorithm is much efficient compared to its previous types
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