The article studies the essence of economic category ‘land-property complex’ in respect to a business entity – enterprise, analyzes theoretical approaches its management and shows approbation methodology strategic at agricultural enterprise. Differences between property land-property complexes were identified classification was provided for management. By using PEST-analysis author estimates de...

Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence and thus satisfy stable Harbourne conjecture. In prime characteristic, can take any radical ideal a ring in regular ring, provided its symbolic powers are given saturations with maximal ideal. Although this property is not suitable for reduction to characteristic p, simi...

We prove that Schur classes of nef vector bundles are limits have a property analogous to the Hodge-Riemann bilinear relations. give number applications, including (1) new log-concavity statements about characteristic (2) and related polynomials (3) another proof normalized Lorentzian.

Let K be an algebraically closed field of characteristic zero and let I = (f1, . . . , fn) be a homogeneous R+-primary ideal in R := K[X, Y, Z]. If the corresponding syzygy bundle Syz(f1, . . . , fn) on the projective plane is semistable, we show that the Artinian algebra R/I has the Weak Lefschetz property if and only if the syzygy bundle has a special generic splitting type. As a corollary we...

An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond precisely to the possible Hilbert functions of Artinian Gorenstein algebras with the Weak Lefschetz Property, a property shared by most Artinian Gorenstein algebras. Starting with an arbitrary SI-sequence, we construct a reduced, arithmeti...

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

We study how solid closure in mixed characteristic behaves after taking ultraproducts. The ultraproduct will be chosen so that we land in equal characteristic, and therefore can make a comparison with tight closure. As a corollary we get an asymptotic version of the Hochster-Roberts invariant theorem in dimension three: if R is a mixed characteristic (cyclically) pure 3-dimensional local subrin...

In reality networks may have random property, small-world property and scale-free property, so in this paper we introduce the heterogeneous network model. We construct the heterogeneous network based on ER random network, WS small-world network and BA scale-free network. Then we use the random rules to interconnect the three sub networks that generate the heterogeneous network. By analyzing the...

Codimension two Artinian algebras have the strong and weak Lefschetz properties provided characteristic is zero or greater than socle degree. It open to what extent such results might extend codimension three Gorenstein algebras. Despite much work, property for algebra has remained largely mysterious; our build on strengthen some of previous results. We here show that every standard-graded A ha...

A splinter is a notion of singularity that has seen numerous recent applications, especially in connection with the direct summand theorem, mixed characteristic minimal model program, Cohen–Macaulayness absolute integral closures and cohomology vanishing theorems. Nevertheless, many basic questions about these singularities remain elusive. One outstanding problem whether property spreads from p...