We present a set-theoretic version of some basic dilation results operator theory. The we have considered are Wold decomposition, Halmos dilation, Sz. Nagy inter-twining lifting, commuting and non-commuting dilations, BCL theorem, etc. point out natural generalizations variations.

This research uses an ordered-response model to evaluate the factors that impact bicycle frequency use for an individual’s commute to and from work. The data used for this paper were gathered during an original survey effort conducted over the Internet in 2002. The paper presents empirical results and discusses the policy implications of these results for urban planning. In addition, the paper ...

Formal power series over non-commuting variables have been investigated as representations of the behavior of automata with multiplicities. Here we introduce and investigate the concepts of aperiodic and of star-free formal power series over semirings and partially commuting variables. We prove that if the semiring K is idempotent and commutative, or if K is idempotent and the variables are non...

We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using BargmannFock representations with commuting and non-commuting variables, the differential calculi being q-deformed in both cases. For q = −1 we obtain a new form of Grassmann-like path integral. on leave of absence from Nuclear Physics Institute, Moscow State Uni...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

Objective: This paper describes a behavior change intervention that encourages active commuting using electrically assisted bikes (e-bikes) for health promotion in the workplace. This paper presents the preliminary findings of the intervention's impact on improving employee well-being and organizational behavior, as an indicator of potential business success. Method: Employees of a UK-based org...

 Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors.  The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero  zero-divisors of  $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...

Given a complex idempotent matrix A, we derive simple, sufficient and necessary conditions for X being nontrivial solution of the Yang-Baxter-like equation AXA = XAX, discriminating commuting solutions from non-commuting ones. On this basis, construct all nonlinear equation.