Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

We show that for a given exact category, there exists bijection between semibricks (pairwise Hom-orthogonal set of bricks) and length wide subcategories (exact extension-closed abelian subcategories). In particular, we category is if only simple objects form semibrick, is, the Schur's lemma holds.

In this paper, using the exact expression for the pairwise error probability derived in terms of the message symbol distance between two message vectors rather than the codeword symbol distance between two transmitted codeword matrices, the exact closed form expressions for the symbol error probability of any linear orthogonal space-time block codes in slow Rayleigh fading channel are derived f...

We propose a flexible sampling method for warp maps used in continuous monotone pairwise alignment of open and closed curves, possibly with landmark constraints. Using the point process machinery, we conduct a detailed study of the sampling method and demonstrate that it prescribes a distribution on the set of warp maps of [0, 1] and the unit length circle S. The distribution (1) possesses the ...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

We give existence results for simple closed curves with prescribed geodesic curvature on S, which correspond to periodic orbits of a charge in a magnetic field.