in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

An efficient synthesis of the N-methylwelwistatin tetracyclic core in only two steps from Kornfeld's ketone is described, whose key transformation involves the generation of a fused bicyclo[4.3.1]decane ring system through a one-pot sequence comprising a Michael-intramolecular aldolization anionic domino process and a DBU-promoted hydrolysis of the N-pivaloyl protecting group. Besides providing...

Ring-structured Bragg fibres that support a single TE-polarisation mode are investigated. The fibre designs consist of a hollow core and rings of holes concentric with the core, which form the low-index layers of the Bragg reflector in the cladding. The effects of varying the air fraction in each ring of holes on the transmission properties of the fibres are analysed and an approximate model ba...

[formula: see text] The enantioselective total synthesis of (+)-laurencin 1 is achieved in 18 steps from (S)-(+)-4-benzyl-3-benzyloxyacetyl-2-oxazolidinone. The key steps in this synthesis are an asymmetric glycolate alkylation leading to acyl oxazolidinone 2 and a subsequent ring-closing olefin metathesis to construct the oxocene core of 1. The approach to medium ring ethers utilized in this s...

In the present paper a novel structure for optical channel drop filter (CDF) based on photonic crystal ring resonator with circular core has been proposed. In order to design the proposed CDF, the plan wave expansion (PWE) method is applied for calculation of band structure and photonic band gap while the transmission characteristics of proposed CDF have been calculated using the finite differe...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

We capture the decay of a quantized vortex ring in superfluid helium-4 by imaging particles trapped on the vortex core. The ring shrinks in time, providing direct evidence for the dissipation of energy in the superfluid. The ring with trapped particles collapses more slowly than predicted by an available theory, but the collapse rate can be predicted correctly if the trapping of the particles o...