We consider the cotriple resolution of algebras over operads in differential graded modules. We focus, to be more precise, on the example of algebras over the differential graded Barratt-Eccles operad, and on the example of commutative alegbras. We prove that the geometric realization of the cotriple resolution (in the sense of model categories) gives a cofibrant resolution functor on these cat...

Let I be a square-free monomial ideal of projective dimension one. Starting with the Taylor complex on generators $$I^r$$ , we use discrete Morse theory to describe CW that supports minimal free resolution . To do so, concretely acyclic matching faces complex.

Let M be a monomial ideal in the polynomial ring S = k[x1, . . . , xn] over a field k. We are interested in the problem, first posed by Kaplansky in the early 1960’s, of finding a minimal free resolution of S/M over S. The difficulty of this problem is reflected in the fact that the homology of arbitrary simplicial complexes can be encoded (via the Stanley-Reisner correspondence [BH,Ho,St]) int...

We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in S = k[x1, x2, ..., xn]; this includes the case of powers of the homogeneous maximal ideal (x1, x2, ..., xn) as a special case. In our most general result we prove that for any Borel fixed ideal I generated in...

in this article, an analytical solution is developed to study the free vibration analysis offunctionally graded rectangular nanoplates. the governing equations of motion are derived basedon second order shear deformation theory using nonlocal elasticity theory. it is assumed that thematerial properties of nanoplate vary through the thickness according to the power lawdistribution. our numerical...

We give a new method to construct minimal free resolutions of all monomial ideals. This relies on two concepts: one is the well-known lcm-lattice ideal; other concept called Taylor basis, which describes how resolution can be embedded in resolution. An approximation formula for ideals also obtained.

in this paper, a nonlinear free vibration analysis of thin annular functionally graded (fg) plate integrated with two uniformly distributed actuator layers made of piezoelectric (pzt4) material on the top and bottom surfaces of the annular fg plate is presented based on kirchhoff plate theory. the material properties of the fgm core plate are assumed to be graded in the thickness direction acco...

free vibration of sandwich plates with temperature dependent functionally graded (fg) face sheets in various thermal environments is investigated. the material properties of fg face sheets are assumed to be temperature-dependent and vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. also, the material properties of...