In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

Let k be an algebraically closed field of characteristic not 2 or 3, V a 3-dimensional vector space over k, R a 3-dimensional subspace of V ⊗V , and TV /(R) the quotient of the tensor algebra on V by the ideal generated by R. Raf Bocklandt proved that if TV /(R) is 3-Calabi-Yau, then it is isomorphic to J(w), the “Jacobian algebra” of some w ∈ V . This paper classifies the w ∈ V ⊗3 such that J(...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

 A series of symmetric and asymmetric binuclear α-diimine nickel(II) complexes toward ethylene polymerization were successfully synthesized and characterized by 1HNMR. All the catalysts were typically activated with MAO and displayed good activity at room temperature under 1atm ethylene pressure. The symmetric catalyst containing isopropyl on l...

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

We construct infinite highly arc-transitive digraphs with finite out-valency and whose sets of descendants are digraphs which have a homomorphism onto a directed (rooted) tree. Some of these constructions are based on [4] and [5], and are shown to have universal reachability

Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The is under various names (”Verlet, leap-frog,..”) most used in simulations of complex system Physics and Chemistry, it also applied Astrophysics. His discrete dynamics has same qualities as exact analytic for continuous space time with reversibility, symplecticity conse...