This paper consists of three interconnected parts. Parts I, III study the relationship between the cohomology of a reductive group G and that of a Levi subgroup H . For example, we provide a sufficient condition, arising from Kazhdan–Lusztig theory, for a natural map Ext• G (L,L′)→ Ext• H (LH ,L ′ H ) to be surjective, given irreducible G-modules L,L′ and corresponding irreducible H -modules LH...

Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...

Let M be a complete nonsingular fine moduli space of modules over an algebra S. A set of conditions is given for the Chow ring of M to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal S-module on M . This result is then applied to the varieties GT parametrizing homogeneous ideals of k[x, y] of Hilbert function T , to moduli spa...

Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$ and $M$ $R$-module with Cosupport in $\mathrm{V}(\mathfrak{a})$. We show that is $\mathfrak{a}$-coartinian if only $\mathrm{Ext}_{R}^{i}(R/\mathfrak{a},M)$ artinian for all $0\leq i\leq \mathrm{cd}(\mathfrak{a},M)$, which provides computable finitely many steps to examine $\mathfrak{a}$-coartinianness. also consider the duality...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

Several hundred Tor exit relays together push more than 1 GiB/s of network traffic. However, it is easy for exit relays to snoop and tamper with anonymised network traffic and as all relays are run by independent volunteers, not all of them are innocuous. In this paper, we seek to expose malicious exit relays and document their actions. First, we monitored the Tor network after developing a fas...

Self-reconngurable robots consist of a set of one or more identical autonomous modules that can adapt their shape and function to tasks. We describe a module that can function as a climbing robot, a manipula-tor, or a leg in a multi-legged walker. This module can make autonomous transitions between these states. We present the control algorithms that enable our robot to be a versatile navigator...