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...     

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).     

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 ${\mathbb{L}}_2^{(\alpha ,\beta )}$.     

Some new estimates for the Helgason Fourier transform on rank 1 symmetric spaces

New estimates are proved for the Helgason Fourier transform in the space \(L^{2}(X)\) on certain classes of functions characterized by the spherical modulus of continuity.     

Bridge‐Clamp Bis(tetrazine)s with [N]8 π‐Stacking Interactions and Azido‐s‐Aryl Tetrazines: Two Classes of Doubly Clickable Tetrazines

Click chemistry at a tetrazine core is useful for bioorthogonal labeling and crosslinking. Introduced here are two new classes of doubly clickable s‐aryl tetrazines synthesized by Cu‐catalyzed cross‐coupling. Homocoupling of o‐brominated s‐aryl tetrazines leads to bis(tetrazine)s structurally characterized by tetrazine cores arranged face‐to‐face. [N]₈ π‐stacking interactions are essential to the conformation. Upon inverse electron demand Diels–Alder (iEDDA) cycloaddition, the bis(tetrazine)s produce a unique staple structure. The o‐azidation of s‐aryl tetrazines introduces a second proximal intermolecular clickable function that leads to double click chemistry opportunities. The stepwise introduction of fluorophores and then iEDDA cycloaddition, including bioconjugation to antibodies, was achieved on this class of tetrazines. This method extends to (thio)etherification, phosphination, trifluoromethylation and the introduction of various bioactive nitrogen‐based heterocycles.     

Biosorption of lanthanum from aqueous solutions using magnetic alginate beads

Magnetic alginate beads are potential biosorbent for sorption of lanthanum(III) from an aqueous medium. Batch experiments were carried out to study the equilibrium, kinetics, and thermodynamics of lanthanum sorption. The effects of initial solution pH, initial lanthanum concentration, and temperature on lanthanum sorption were investigated. The optimum pH value was defined to be 4. Kinetic and isotherm experiments were carried out at the optimum pH. It was enough to reach the adsorption equilibrium at 4 hours, and the maximum uptake capacity was (1.8 mmol g^?1) at 25°C. Uptake kinetics and sorption isotherms were obtained and modeled using conventional and simple equations: best results were respectively obtained with the pseudo-second-order rate equation and the Langmuir equation. The La(III) loaded magnetic alginate beads were regenerated using 0.1 M CaCl₂ without activity loss.     

Tetrazo[1,2-b]indazoles: Straightforward Access to Nitrogen-Rich Polyaromatics from s-Tetrazines

The straightforward access to a new class of aza-polyaromatics is reported. Starting from readily available fluorinated s-tetrazine, a cyclization process with azide leads to the formation of an unprecedented tetrazo[1,2-b]indazole or a bis-tetrazo[1,2-b]indazole (cis and trans conformers). Based on the new nitrogen core, further N-directed palladium-catalyzed ortho-C−H bond functionalization allows the introduction of halides or acetates. The physicochemical properties of these compounds were studied by a joint experimental/theoretical approach. The tetrazo[1,2-b]indazoles display solid-state π-stacking, low reduction potential, absorption in the visible range up to the near-infrared, and intense fluorescence, depending on the molecular structure.     

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.