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let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

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_{...

The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group theory analogous to that of good filtrations and tilting modules for GLn(k). This paper is an initial attempt at such a theory. We obtain two sufficient conditi...

Given C-algebras A and B acting cyclically on Hilbert spaces H and K, respectively, we characterize completely isometric A, B-bimodule maps from B(K,H) into operator A, B-bimodules. We determine cogenerators in some classes of operator bimodules. For an injective cogenerator X in a suitable category of operator A, B-bimodules we show: if A, regarded as a Csubalgebra of Al(X) (adjointable left m...

We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained. Keywords—faithfully balanced se...

We explore the concept of self-assembling robot systems consisting of simple passive structural modules plus active robotic modules. In particular, we consider a space of 2and 3-DOF robots with rotating grippers which attach to passive structural bars. The resulting systems range from a passive truss with one independent active climbing module to fully self-reconfiguring dynamic structures comp...

Self-organization is a phenomenon found in biomolecular self-assembly by which proteins are spontaneously driven to assemble and attain various functionalities. This study reports on self-organized behavior in which distributed centimeter-sized modules stochastically aggregate and exhibit a translational wheeling motion. The system consists of two types of centimeter-sized water-floating module...