Related papers: Kolmogorov and Aleksandrov in Sevan Monastery, Arm…

Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook "An Introduction to Kolmogorov Complexity and Its…

Upper bounds on the Kolmogorov distance (and, equivalently in this case, on the total variation distance) between the Student distribution with p degrees of freedom (SD_p) and the standard normal distribution are obtained. These bounds are…

We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds…

We give an example of automated geometry reasoning for an imaginary classroom project by using the free software package GeoGebra Discovery. The project is motivated by a publicly available toy, a rocking camel, installed at a medical…

Study of soft sets was first proposed by Molodtsov in 1999 to deal with uncertainty in a non-parametric manner. The researchers did not pay attention to soft set theory at that time but now the soft set theory has been developed in many…

Mitochondrial DNA from fourteen archaeological samples at the Ural State University in Yekaterinburg, Russia was extracted to test the feasibility of ancient DNA work on their collection. These samples come from a number of sites that fall…

This is a fairy tale taking place in Chessland, located in the Bermuda triangle. The chess pieces survey their land and trap enemy pieces. Behind the story, there is fascinating mathematics on how to optimize surveying and trapping. The…

Reproducing my talk at Algebra Symposium held at Hiroshima University, August 26--29, 2013, I review recent results on super algebraic groups, emphasizing results obtained by myself and my coauthors using Hopf algebraic techniques. The…

In this paper, we show that, under some technical assumptions, the Kolmogorov-Sinai entropy and the permutation entropy are equal for one-dimensional maps if there exists a countable partition of the domain of definition into intervals such…

The 1908 Tunguska event is used to be associated with a forestfall named after its first scientific researcher -- Leonid Kulik.However association of the Kulikovskii forestfall with the events in the morning of June 30, 1908 is based only…

This is an English translation and digitisation of Sophie Kowalevski's (also know as Sofya Kovalevskaya) paper on what is now known as the Kovalevskaya Top. The original paper was written in French and published in Vol 12 of Acta…

The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…

Kolmogorov-Arnold Networks (KANs) have very recently been introduced into the world of machine learning, quickly capturing the attention of the entire community. However, KANs have mostly been tested for approximating complex functions or…

Vishaps -- dragon stones -- discovered in the Armenian Highlands convey a remarkable message about the spiritual and social character of their epoch, c. 4000 BC. The unexpected bimodal distribution of their elevations indicates the…

Recently, Mikheyev et al. (2019) have produced a preprint study describing the genomes of nine Khazars archeologically dated from the 7th to the 9th centuries found in the Rostov county in modern-day Russia. Skull morphology indicated a mix…

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not…

First the crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, there exists no abstract theory of probabilities, simply because the factual concept of probability is itself unachieved:…

Let $X$ be a random variable and define its concentration function by $$\mathcal{Q}_{h}(X)=\sup_{x\in \mathbb{R}}\mathbb{P}(X\in (x,x+h]).$$ For a sum $S_n=X_1+\cdots+X_n$ of independent real-valued random variables the Kolmogorov-Rogozin…

Let $\mathbf D$ be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On $\BZ\mathbf D$ we define a product and a coproduct, together with an internal product, that is,…

In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are associated to $p$-adic representations over number fields. We now…