Related papers: Berezovsky number
Some mathematical properties of the Erd\"os number and its formal equivalents are shown. An informetric equivalent is presented: the Rousseau number. This contribution honors Ronald Rousseau for his 73th birthday.
We study networks of processes which all execute the same finite-state protocol and communicate thanks to a rendez-vous mechanism. Given a protocol, we are interested in checking whether there exists a number, called a cut-off, such that in…
We prove a curious identity for the Bernoulli numbers.
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
Chernoff information upper bounds the probability of error of the optimal Bayesian decision rule for $2$-class classification problems. However, it turns out that in practice the Chernoff bound is hard to calculate or even approximate. In…
The Motzkin numbers can be derived as coefficients of hybrid polynomials. Such an identification allows the derivation of new identities for this family of numbers and offers a tool to investigate previously unnoticed links with the theory…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
Random networks generators like Erdoes-Renyi, Watts-Strogatz and Barabasi-Albert models are used as models to study real-world networks. Let G^1(V,E_1) and G^2(V,E_2) be two such networks on the same vertex set V. This paper studies the…
The closed-form solution for the average distance of a deterministic network--Sierpinski network--is found. This important quantity is calculated exactly with the help of recursion relations, which are based on the self-similar network…
We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers…
Bitcoin is a digital currency and electronic payment system operating over a peer-to-peer network on the Internet. One of its most important properties is the high level of anonymity it provides for its users. The users are identified by…
This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.
In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise…
Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard-Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.