Describing the properties of the minimal free resolution of a monomial ideal I is a difficult problem posed in the early 1960’s. The main directions of progress on this problem were: • constructing the minimal free resolutions of special monomial ideals, cf. [AHH, BPS] • constructing non-minimal free resolutions; for example, Taylor’s resolution (cf. [Ei, p. 439]) and the cellular resolutions •...

We determine the simplicial complexes ∆ whose Stanley-Reisner ideals I∆ have the following property: for all n ≥ 1 the powers In ∆ have linear resolutions and finite length local cohomologies.

Using certain finite-dimensional stable range of the nonlinear terms, we obtain large families of exact solutions parameterized by functions for the equation of nonstationary transonic gas flows discovered by Lin, Reisner and Tsien, and its three-dimensional generalization.

In prime characteristic there are important invariants that allow us to measure singularities. For certain cases, it is known they rational numbers. this article, we show property for Stanley-Reisner rings in several cases.

The first, fully non linear, mean field theory of relativistic gravitation has been developed in 2004. The theory makes the striking prediction that averaging or coarse graining a gravitational field changes the matter content of space-time. A review of the general theory is presented, together with new calculations that highlight this effect on black holes of the Reisner-Nordström (RN) family....

In 1974, the author proved that codimension of ideal (g1,g2,…,gd) generated in group algebra K[Zd] over a field K characteristic 0 by generic Laurent polynomials having same Newton polytope Γ is equal to d!×Volume(Γ). Assuming Newtons simplicial and super-convenient (that is, containing some neighborhood origin), strengthens 1974 result explicitly specifying set Bsh monomials cardinality d!×Vol...