let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

This work focuses on a mechanism (and software) which communicates (via MathLink protocol) and provides compatibility between the representation of nonlinear functions specified as Mathematica expressions and objects of suitable classes supported by the C-XSC automatic differentiation modules. The application of the developed communication software is demonstrated by MathLink compatible program...

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field k of positive characteristic p. The main result proves that Weyl modules have (cogood) p-filtrations subject to restrictions on p. In case the high weight of the Weyl module is p-regular, the p-filtration is compatible with theG1-radical series of the module. This is a preliminary...

We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebra structures on the Witt algebra are classified. All of them are simple and they in...

We use weights on objects in an abelian category to define what we call a path metric. introduce three special classes of weight: those compatible with short exact sequences; induced by their metric; and which bound prove that these conditions are fact equivalent, such exact. As case metric, obtain distance for generalized persistence modules whose indexing is measure space. this Wasserstein di...

We present the programming language Keris, an extension of Java with explicit support for software evolution. Keris introduces extensible modules as the basic building blocks for software. Modules are composed hierarchically revealing explicitly the architecture of systems. A distinct feature of the module design is that modules do not get linked manually. Instead, the wiring of modules gets in...