Write I(G) for the set of independent sets of a graph G and i(G) for |I(G)|. It has been conjectured (by Alon and Kahn) that for an N -vertex, d-regular graph G, i(G) ≤ ( 2 − 1 )N/2d . If true, this bound would be tight, being achieved by the disjoint union ofN/2d copies ofKd,d. Kahn established the bound for bipartite G, and later gave an argument that established i(G) ≤ 2 N 2 (1+ 2 d) for G n...

One discovers why Morgan Ward solution [1] of ψ-difference calculus nonhomogeneous equation ∆ ψ f = ϕ in the form f (x) = n≥1 B n n ψ ! ϕ (n−1) (x) + ψ ϕ(x) + p(x) recently proposed by the present author (see-below)-extends here now to ψ-Appell polynomials case-almost automatically. The reason for that is just proper framework i.e. that of the ψ-Extended Finite Operator Calculus(EFOC) recently ...

At the first part of our communicate we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Morgan Ward solution of uncountable family of ψ-difference calculus nonhomogeneous equations ∆ ψ f = ϕ in the form f (x) = n≥1 B n n ψ ! ϕ (n−1) (x) + ψ ϕ(x) + p(x) extends to...

ENWEndNote BIBJabRef, Mendeley RISPapers, Reference Manager, RefWorks, Zotero AMA Hollingdale K, Firebaugh CM, Morgan SM. A brief report relating physical activity and depressive symptoms in women during the COVID-19 pandemic. Human Movement. 2023;24(1):100-103. doi:10.5114/hm.2023.118003. APA Hollingdale, K., Firebaugh, C. M., & Morgan, S. M. (2023). Movement, 24(1), 100-103. https://doi.org/1...