let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

A module M is called ?-?ss-supplemented if every submodule X of has a ?ss-supplement Y in which direct summand such that + = and ? Soc? (Y) where Soc?(Y) the sum simple ?-small submodules Y? for some M. Moreover, completely ?-?ss-supplemented. Thus, we present two new types algebraic structures are stronger than ?-D11 ?-D+11-modules, respectively. In this paper investigate basic properties, dec...

In mid-2004, it was decided that the list of optional modules available to students taking the MSc programme in Computing, Internet Law and Management at King’s College London (KCL) should be supplemented with a module in computer forensics (CF) and cybercrime. It was proposed that this module should be delivered as a reading course to be assessed by means of a dissertation and a linked viva vo...

We study syndetic sensitivity and mean for linear dynamical systems. For the aspect, we obtain some properties of adjoint operators left multiplication operators. also show that there exists a system (X×Y,T×S) such is cofinitely sensitive but (X,T) (Y,S) are not syndetically sensitive. if sensitive, where Y complex Banach space, spectrum T meets unit circle. results regarding perturbations.

We report the discovery of TOI-1444b, a 1.4-$R_\oplus$ super-Earth on 0.47-day orbit around Sun-like star discovered by {\it TESS}. Precise radial velocities from Keck/HIRES confirmed planet and constrained mass to be $3.87 \pm 0.71 M_\oplus$. The RV dataset also indicates possible non-transiting, 16-day ($11.8\pm2.9M_\oplus$). tentative detection phase curve variation secondary eclipse TOI-144...