A bstract We present, for the first time, complete off-shell 4 D, $$ \mathcal{N} N = 2 superfield actions any free massless integer spin s ≥ fields, using harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields {h}_{\alpha \left(s-1\right)\dot{...

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...

Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...

Let $p(z)$ be a polynomial of degree $n$. Then the polar derivative with respect to real or complex number $\alpha$ is defined by $D_\alpha p(z)=n p(z)+(\alpha-z) p^{\prime}(z)$. Govil and Mctume [14] proved that if $n$ having all its zeros in $|z| \leq k, k \geq 1$, then for $|\alpha| 1+k+k^n$,$$\begin{aligned}\max _{|z|=1}\left|D_\alpha p(z)\right| & n\left(\frac{|\alpha|-k}{1+k^n}\right)...

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

In this paper, we introduce a new quantum divergence$$\Phi (X,Y) = \Tr \left[\left(\dfrac{1-\alpha}{\alpha}+ \dfrac{\alpha}{1-\alpha}\right)X+2Y - \dfrac{X^{1 -\alpha}Y^{\alpha}}{\alpha}- \dfrac{X^{\alpha}Y^{1-\alpha}}{1-\alpha} \right],$$where $0< \alpha <1$.We study the least square problem with respect to divergence. We also show that divergence satisfies Data Processing Inequa...

Let \(M= \Gamma \setminus \mathbb {H}_d\) be a compact quotient of the d-dimensional Heisenberg group \(\mathbb by lattice subgroup \(\Gamma \). We show that eigenvalue counting function \(N^\alpha \left( \lambda \right) \) for any fixed element family second order differential operators \(\left\{ \mathcal {L}_\alpha \right\} on M has asymptotic behavior \sim C_{d,\alpha } {\text {vol}}\left( M...

The aim of this work is to introduce and study the notions Hom-pre-Jordan algebra Hom-J-dendriform which generalize Hom-Jordan algebras. algebras are regarded as underlying algebraic structures behind Rota-Baxter operators O-operators introduced in paper. also analogues Hom-pre-Lie for anti-commutator a left multiplication operator gives representation algebra. On other hand, analogue Hom-dendr...