Let $K$ be a field of characteristic zero, $X_n=\{x_1,\dots,x_n\}$ set variables, $K[X_n]$ the polynomial algebra and $F_n$ free metabelian Lie rank $n$ generated by $X_n$ over base $K$. Well known result Weitzenb\"ock states that $K[X_n]^\delta=\big \{u\in K[X_n] \big\vert\ \delta(u)=0\big \}$ is finitely as an algebra, where $\delta$ locally nilpotent linear derivation $K[X_n]$. Extending thi...

Using the notion of a symmetric virtual diagonal for Banach algebra, we prove that algebra is symmetrically amenable if its second dual amenable. We introduce operator amenability in category completely contractive algebras as an analogue algebras. give some equivalent formulations and investigate hereditary properties show locally compact groups to Fourier algebra. Finally, discuss about Jorda...

The building and construction sector is vital in Jordan. Over the past decade it witnessed rapid growth. Single-family housing is a popular option in Jordan. The construction sector consumes large amounts of energy and resources. Green and energy efficient buildings are growing in popularity and there are policies adopted to encourage energy efficient buildings. These buildings are often justif...

Revised delta(34)S reference values with associated expanded uncertainties (95% confidence interval (C.I.)) are presented for the sulfur isotope reference materials IAEA-S-2 (22.62 +/- 0.16 per thousand) and IAEA-S-3 (-32.49 +/- 0.16 per thousand). These revised values are determined using two relative-difference measurement techniques, gas source isotope ratio mass spectrometry (GIRMS) and dou...

The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) ⊆ L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T (A2n+1) = 2n+1 ∑ i=1 (−1)i+1Ai−1T (A)A2n+1−i, for all A ∈ A(X) and some fixed integer n ≥ 1. In this case T ...

The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...

We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density l...