A polarization splitter and rotator that is compatible with optical integration is presented. In contrast to prior efforts to achieve this functionality, the adiabatic nature of this approach allows for nearly ideal performance over the 1.5-1.6μm regime. c © 2003 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (130.2790) Guided Waves High index contrast waveguides a...

Let $R$ be a commutative ring with identity‎. ‎A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$‎, ‎$a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...

for all x ∈ X . Quasi-isometries occur naturally in the study of the geometry of discrete groups since the length spaces on which a given finitely generated group acts cocompactly and properly discontinuously by isometries are quasi-isometric to one another [Gro]. Quasi-isometries also play a crucial role in Mostow’s proof of his rigidity theorem: the theorem is proved by showing that equivaria...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

Let R be a commutative ring with identity. In this paper we define the notion of almost primary ideal. An ideal of a ring R is said to be an almost primary ideal if for a, b ∈ R with ab ∈ I − I2 then a ∈ I or bn ∈ I for some n ∈ N. We prove that in Noetherian domains almost primary ideals are primary. Mathematics Subject Classification: 13A15

The classification of quasi primary fields is outlined. It is proved that the only conserved quasi primary currents are the energy momentum tensor and the O(N)Noether currents. Derivation of all quasi primary fields and the resolution of degeneracy is sketched. Finally the limits d = 2 and d = 4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so. (T...