Growth properties of the q-Dunkl transform in the space $$L^{p}_{q,\alpha }({\mathbb {R}}_{q},|x|^{2\alpha +1}d_{q}x)$$ L q , α p ( R q , | x | 2 α + 1 d q x )

The Ramanujan Journal - Our aim in this work is to prove an analogue of Titchmarsh’s theorem [19, Theorem 84] and Younis’s theorem [20, Theorem 3.3] on the image under the q-Dunkl...     

Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on [0,π]

Our aim in this paper is to prove an analog of the classical Titchmarsh theorem on the image under the discrete Fourier–Jacobi transform of a set of functions satisfying a generalized Lipschitz condition in the space ${\mathbb{L}}_2^{(\alpha ,\beta )}$.     

First-principles study of structural,electronic, thermodynamic,and thermoelectric properties of a new ternary half-Heusler alloy PdZrGe

This work concerns a predictive study of PdZrGe half-Heusler compound with 18 valence electrons. The structural and electronic properties are investigated by using the full potential linearized augmented plane wave (FP-LAPW) method within the framework of generalized gradient approximation (GGA). To investigate the thermodynamic properties, we are applying the quasi-harmonic Debye model. The semi-classical Boltzmann theory as implemented in the BoltzTraP code is used to study the thermoelectric properties. We have found that the PdZrGe alloy is an indirect band gap semiconductor. Also the PdZrGe exhibit a negative thermal expansion. The Seebeck coefficient (S) is relatively high (237 µV/K at 300?K) due to its semiconducting nature. The calculated thermoelectric figure of merit is 0.759 at 300?K; this result indicates that our compound is an excellent candidate for practical applications in the thermoelectric field.     

Virtual Excitations and Entanglement Dynamics and Polygamy in Three Ultra-Strongly Coupled Systems

The Milburn dynamics of three non resonant ultra-strongly coupled oscillators are resolved by using symplectic geometry. The Milburn dynamics of virtual excitations and how they affect the pairwise entanglement are looked at. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, it is shown that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, the effects of physical parameters on the redistribution of virtual excitations among the three bi-partitions are analyzed. As a result, the violation of the monogamy of excitations is shown as in quantum discord. This implies that excitations can be considered as signatures of quantum correlations beyond entanglement. Besides, it is emphasized that the treatment can be used to model coupled quantum circuits in real situations (with decoherence).