let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

The Wicked Problem of Forest Policy: A Multidisciplinary Approach to Sustainability in Landscapes. Nikolakis W., and J. L. Innes, editors. 2020. Cambridge University Press, Cambridge, U.K. x + 400 pp. £64.99 (hardcover). ISBN 978-1-108-47140-4. Sustainable Governance Wildlife Community Based Natural Resource Management. Child, B. 2019. Routledge, Abingdon, Oxon, xxiv 381 £37.99 (paperback). 978...

We investigate the local regularity of pointed spacetimes, that is, timeoriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein vacuum spacetimes. Under curvature and injectivity bounds only, we establish the existence of a local coordinate chart defined in a ball with definite size in wh...

Broadband communications lie at the heart of the developing information society. Employing a logistic diffusion model, we analyze the factors that influence the diffusion of fixed and mobile broadband. For fixed broadband diffusion, we find that local loop unbundling, income, population density, education, and price are significant factors of fixed broadband diffusion. For mobile broadband, mul...