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Full-Text Articles in Computer Sciences
Summation Of Divergent Infinite Series: How Natural Are The Current Tricks, Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich
Summation Of Divergent Infinite Series: How Natural Are The Current Tricks, Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Infinities are usually an interesting topic for students, especially when they lead to what seems like paradoxes, when we have two different seemingly correct answers to the same question. One of such cases is summation of divergent infinite sums: on the one hand, the sum is clearly infinite, on the other hand, reasonable ideas lead to a finite value for this same sum. A usual way to come up with a finite sum for a divergent infinite series is to find a 1-parametric family of series that includes the given series for a specific value p = p0 of the …
Why Zipf's Law: A Symmetry-Based Explanation, Daniel Cervantes, Olga Kosheleva, Vladik Kreinovich
Why Zipf's Law: A Symmetry-Based Explanation, Daniel Cervantes, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we have probability distributions for which, for large values of the corresponding quantity x, the probability density has the form ρ(x) ~ x−αfor some α > 0. While, in principle, we have laws corresponding to different α, most frequently, we encounter situations -- first described by Zipf for linguistics -- when α is close to 1. The fact that Zipf's has appeared frequently in many different situations seems to indicate that there must be some fundamental reason behind this law. In this paper, we provide a possible explanation.