SOME RESULTS OF GENERALIZED LEFT (θ,θ)-DERIVATIONS ON SEMIPRIME RINGS

Let R be an associative ring with center Z(R) . In this paper , we study the commutativity of semiprime rings under certain conditions , it comes through introduce the definition of generalized left(θ,θ)- derivation associated with left (θ,θ) -derivation , where Î¸ is a mapping on R

( U,R) STRONGLY DERIVATION PAIRS ON LIE IDEALS IN RINGS

Let R be an associative ring , U be a nonzero Lie ideal of R. In this paper , we will present the definition of (U,R) strongly derivation pair (d,g) , then we will get d=0 (resp. g=0 ) under  certain conditions on d and g for (U,R) strongly derivation pair (d,g) on semiprime ring . After that we will study prime rings , semiprime rings ,and rings  that have a commutator left nonzero divisor with (U,R) strongly derivation pair (d,g) , to obtain the notation of  (U,R) derivation

Commutativity of Addition in Prime Near-Rings with Right (θ,θ)-3-Derivations

Let N be a near-ring and  is a mapping on N . In this paper we introduce the notion of right ()-3-derivation in near-ring N. Also, we investigate the commutativity of addition of prime near-rings satisfying certain identities involving right ()-3-derivation

On Generalized (θ, θ) -3 -Derivations in Prime Near-Rings

Let N be a near-ring and is a mapping on N . In this paper we introduce the notion of generalized (θ, θ)-3-derivation in near-ring N . Also we investigate the commutativity of addition of near-rings satisfying certain identities involving generalized (θ,θ)-3-derivation on prime near-rings

Jordan (θ, θ)*- Derivation Pairs of Rings With Involution

Let  R be a 6-torsion  free ring with involution , θ  is a mapping of R and let (d,g) : R→R be an additive mapping . In this paper  we will give the relation between (θ, θ)*-derivation pair and Jordan (θ, θ)*-derivation pair . Also , we will prove that if (d,g) is a Jordan (θ, θ)*-derivation pair , then d is a Jordan (θ, θ)*-derivation

Jordan left (?,?) -derivations Of ?-prime rings

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true

Transesterification in Epoxy-Thiol Exchangeable Liquid Crystalline Elastomers

The incorporation of vitrimer bond-exchange chemistry into liquid crystalline elastomer networks produces ‘exchangeable liquid crystal elastomers’ (xLCE). These materials offer a facile method of material re-shaping and alignment post-polymerisation via the application of a mechanical stress above the temperature of activation of bond exchange. We use di-epoxy mesogenic monomers with thiol-terminated spacers and crosslinker to investigate a range of resulting xLCE. The “click” chemistry of thiols results in good control over the network topology, and low glass transition in this family of materi-als. By combining different spacers, we were able to obtain smectic and nematic phases, and adjust the liquid crystal to iso-tropic phase transition between 42 and 140 °C, while the elastic-plastic transition temperature was maintained close to 200 °C. The broad gap between these temperatures ensures that thermally actuating uniformly aligned elastomers are stable and show no residual plastic creep, making epoxy-thiol xLCE promising for a range of engineering applications.ERC H202

Liquid Crystalline Vitrimers with Full or Partial Boronic-Ester Bond Exchange

In this manuscript, a new vitrimer chemistry strategy (boronic transesterification) is introduced into liquid crystal elastomers (LCEs) to allow catalyst-free bond exchange to enable processing (director alignment, remolding, and welding) in the liquid crystalline (nematic) phase. Additionally, the concept of partial vitrimer network is explored, where a percolating fraction of the network remains permanently cross-linked, hence preserving the integrity of the materials and preventing large creep. This combined strategy allows one to avoid the shortcomings of current methods of aligning LCE, especially in complex shapes. Thiol-acrylate Michael addition reaction is used to produce uniform polymer networks with controllable thermomechanical response and local plasticity. Control of the plasticity is achieved by varying the fractions of permanent and exchangeable network, where a material “sweet spot” with an optimum elastic/plastic balance is identified. Such exchangeable LCE (xLCE) allows postpolymerization processing, while also minimizing unwanted creep during actuation. Moreover, conjoining multiple materials (isotropic and liquid-crystalline) in a single covalently bonded composite structure results in a variety of smart morphing systems that adopt shapes with complex curvature. Remolding and welding xLCEs may enable the applications of these materials as mechanical actuators in reversibly folding origami, in vivo artificial muscles, and in soft robotics