Let R be a prime ring with center Z, I nonzero ideal of and D: × → symmetric bi–(α, α)-derivation d the trace D. In present paper, we have considered following conditions: i) [d(x), x]α,α = 0, ii)[d(x), ⊆ Cα,α, iii)(d(x), x)α,α iv)D1(d2(x), x) v)d1(d2(x)) f(x), for all x, y ∈ I, where D1 D2 are two bi-(α, α)-derivations, d1, d2 traces D1, respectively, B: is bi-additive mapping, f B.

The design and facile synthesis of sterically constrained new analogs of PNA having gem-dimethyl substitutions on glycine (dmg-PNA-T) is presented. The PNA oligomers [aminoethyl dimethylglycyl (aedmg) and aminopropyl dimethylglycyl (apdmg)] synthesized from the monomers 6 and 12) effected remarkable stabilization of homothyminePNA(2):homoadenine DNA/RNA triplexes and mixed base sequence duplexe...

The full transformation semigroup TnTn is defined to consist of all functions from Xn={1,…,n}Xn={1,…,n} itself, under the operation composition. In \cite{JMH1}, for any αα in TnTn, Howie and denoted collapse by c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}. Let OnOn be order-preserving transformations CnCn decreasing on XnXn=under its natural order, respectively. E(On)E(On) set ide...

We introduce order-k α-hulls and αshapes — generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape p...