We show that any finite triangulation of the real projective plane or dunce hat is partitionable. To prove this, we introduce simple yet useful gluing tools allow us to reduce partitionability a given complex smaller constituent relative subcomplexes such as disk open M\"obius strip. The process generates partitioning schemes with distinctive shelling/constructible flavor. also give tool lift s...

BACKGROUND The hybrid war of Russia against Ukraine has been started in certain districts of Donetsk and Luhansk oblasts within the Donbas area in 2014. CASE PRESENTATION We report a clinical case of a combat patient who was injured after the multiple launcher rocket system "Grad" shelling, diagnosed with hydrodynamic liver rupture followed by medical management with application of damage con...

Each rule f that assigns a vector f(G) to an (n+1)-graphG determines a class (or property) of n-manifold invariants. An invariant v = v(M) is in this class if, for any triangulated manifold |G| = M , one has that v(M) is a linear function of f(G). This paper defines a flag vector f(G) for i-graphs, whose associated invariants might be quantum, and which is of interest in its own right. The defi...

The linear span of isomorphism classes of posets, P, has a Newtonian coalgebra structure. We observe that the ab-index is a Newtonian coalgebra map from the vector space P to the algebra of polynomials in the non-commutative variables a and b. This enables us to obtain explicit formulas showing how the cd-index of the face lattice of a convex polytope changes when taking the pyramid and the pri...

This paper attempts to provide an additional insight into properties of exceedances and placement statistics described in Bairamov and Eryılmaz (2000). The importance of these concepts in construction of non-parametric tests of equality (identity) of distributions has been demonstrated by Katzenbeisser (1985), (1986), Matveychuk and Petunin (1990), Johnson and Kotz (1991), (1994), Wesolowsky an...

The physico-chemical characteristics as well as chemical composition of Arachis hypogaea shell (AHS) ash were evaluated by different techniques such as X-Ray fluorescence, X-Ray diffraction and thermo-gravimetry. The material, which is considered a by-product obtained from Groundnut shelling, was investigated as a potential fertilizer, energy source and as animal feeds. And this will provide a ...