We construct a directed social network of coaches based on tutelage, from which we examine community structure based upon connections in the network given by community-detection algorithms. We use this approach to investigate communities of coaches from the National Football League for American football and Major League Baseball, both sports leagues in the United States. We analyse patterns amo...

We establish a general form of sum-difference inequality in two variables, which includes both two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities consid...

Define f on the integers n > 1 by the recurrence f(n) mAn{n, minm[ 2f(m) + 3f(n/m)}. The function f has f(n) n as its upper envelope, attained for all prime n. The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form f(n) C(logn)1+1/ for certain constants and C, in the sense that for any > 0, the inequality f(n) <_ (C+)(logn) 1+1/’ holds for in...

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its applications to time operators and abstract Dirac operators are also investigated.

Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.

The rise of social media platforms has fundamentally altered the public discourse by providing easy to use and ubiquitous forums for the exchange of ideas and opinions. Elected officials often use such platforms for communication with the broader public to disseminate information and engage with their constituencies and other public officials. In this work, we investigate whether Twitter conver...

In this note we prove a discrete analogue of the continuous Halanay inequality and apply it to derive sufficient conditions for the global asymptotic stability of the equilibrium of certain generalized difference equations. The relation with some numerical schemes for functional delay differential equations is discussed.

So far there have been few results presented on the attracting and quasi-invariant sets for impulsive stochastic difference equations with continuous time. The main aim of this work is to close this gap. By establishing a difference inequality with continuous time, we obtain the attracting and quasi-invariant sets of systems under consideration. An example is given to illustrate the theory. Mat...

In the paper, it analyses the relationship between social capital and social security among the youth in sari(Northern Iran). Out of 65326 young people more than 118 ones were randomly selected through Cochran sampling method.The Alph- coranbach coefficient for the social capital were %85 and for social security were %83. According to Pearson correlation coefficient, there is a significant rela...