We study monomial ideals with linear presentation or partially resolution. give combinatorial characterizations of for square-free degree 3, and primary whose resolutions are except the last step (the “almost linear” case). also sharp bounds on Castelnuovo–Mumford regularity numbers generators in some cases. It is a basic observation that linearity properties inherited by restriction an ideal t...

For a simplicial complex $K$ with $m$ vertices, there is canonical $\mathbb Z_2^m$-space known as real moment angle R \mathcal Z_K$. In this paper, we consider the quotient spaces $Y=\mathbb Z_K / \mathbb Z_2^{k}$, where pure shellable and Z_2^k \subset Z_2^m$ maximal free action on A typical example of such small cover, cover topological analog toric manifold. We compute integral cohomology gr...

With connection with the full-scale Russian military aggression, issue of clear spatial fixation violations natural complexes and their components has become extremely urgent. The consequences projectiles rockets, fires that arose as a result shelling, fortification activities, etc. led to direct disturbance landscapes, well chemical pollution. This, in turn, an negative impact on state environ...

The present investigation for studying correlations and path analysis estimates grain yield contributing characters in maize was carried out at Maize Research Centre Seed Farm, Devihosur eleven characters. Days to 50 per cent tasseling significantly positively correlated with days silking negatively plant height, ear cob length, shelling percentage, hundred weight yield. significant percentage ...

Consider a polygon P and all neighboring circles (circles going through three consecutive vertices of P ). We say that a neighboring circle is extremal if it is empty (no vertices of P inside) or full (no vertices of P outside). It is well known that for any convex polygon there exist at least two empty and at least two full circles, i.e. at least four extremal circles. In 1990 Schatteman consi...

We develop an iterated homology theory for simplicial complexes. This theory is a variation on one due to Kalai. For 1 a simplicial complex of dimension d − 1, and each r = 0, . . . , d , we define r th iterated homology groups of 1. When r = 0, this corresponds to ordinary homology. If 1 is a cone over 1′, then when r = 1, we get the homology of 1′. If a simplicial complex is (nonpure) shellab...

It is clear that the random variable νm shows the number of the elements of the sample Y1, Y2, ..., Ym falling into random interval (f1(X1, X2, ..., Xn), f2(X1, X2, ..., Xn). We call νm the exceedance statistics in independent and identically distributed (iid) sequences of observations. We are interested in distributional properties of νm. The particular cases for the lower and upper thresholds...

Nonblinking excitonic emission from near-infrared and type-II nanocrystal quantum dots (NQDs) is reported for the first time. To realize this unusual degree of stability at the single-dot level, novel InP/CdS core/shell NQDs were synthesized for a range of shell thicknesses (~1-11 monolayers of CdS). Ensemble spectroscopy measurements (photoluminescence peak position and radiative lifetimes) an...

The augmented Bergman complex of a matroid is simplicial introduced recently in work Braden, Huh, Matherne, Proudfoot and Wang. It may be viewed as hybrid two well-studied pure shellable complexes associated to matroids: the independent set complex.
 shown here that also shellable, via different families shelling orders. Furthermore, comparing description its homotopy type induced from she...