The Abstract Compactness Theorem of Makowsky and Shelah for model theoretic logics is shown to be an immediate consequence of a general characterization of topological spaces having [ ; ]-compact products, when applied to spaces of structures endowed with the natural topology induced by the de…nable classes of a logic L. In this context, the notion of an ultra…lter U being related to L correspo...

in current study, seven organic fertilizers including; leaf mold (lm), rice husk (rh), manure, spent mushroom compost (smc), mixture of lm, rh and smc (m 1), mixture of lm, rh and manure (m 2) with the ratio of 1:1:1 and control (no fertilizer) along with some levels of soil compactness comprising roller weights of 36, 56, 76 kilogram were used. treatments were applied in a strip plot design wi...

Interval routing is a popular compact routing method for point-to-point networks which found industrial applications in novel transputer routing technology 13]. Recently much eeort is devoted to relate the eeciency (measured by the dilation or the stretch factor) to space requirements (measured by the compactness or the total number of memory bits) in a variety of compact We add new results in ...

In this paper, we are concerned with the following critical fractional Choquard equation$ (-\Delta)^{s}u + V(x)u = (\mathcal{K}_{\mu}*|u|^{2^{*}_{\mu,s}})|u|^{2^{*}_{\mu,s}-2}u, \ u \in D^{s,2}(\mathbb{R}^{N}), $where $ s\in (0,1) $, N\geq 3 \max\{N-4s, 0\}<\mu<N 2^{*}_{\mu,s} \frac{2N-\mu}{N-2s} V(x) is a potential function, and \mathcal{K}_{\mu} Riesz potential. first part of combining ...