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

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.     

Evaluation of [Co(gly)3]- as a 35Cl- NMR shift reagent for cellular studies

We studied the efficacy of the tris-glycinatocobaltate(II) complex ([Co(gly)(3)](-)) as a shift reagent (SR) for chloride by (35)Cl NMR spectroscopy and compared to that of Co(2+)((aq)). Due to the relatively low thermodynamic stability of [Co(gly)(3)](-), a 1:3 Co(II)/gly stoichiometric solution at physiological pH is approximately a 2:1 mixture of [Co(gly)(2)(H(2)O)(2)] and [Co(gly)(H(2)O)(4)](+). This SR was found to be stable up to higher pH values than Co(2+)((aq)), better preventing Co(OH)(2) formation at alkaline pH. No significant differences in the (35)Cl(-) NMR chemical shift induced by Co(II)/gly or Co(2+)((aq)) were observed in the presence of physiological concentrations of either Ca(2+) or Mg(2+), or of either Na(+) or K(+). Although Co(2+)((aq)) was almost twice as effective as Co(II)/gly in shifting the (35)Cl(-) NMR resonance at the same high rho ([SR]/[Cl(-)]) value and low ionic strength, Co(2+)((aq)) showed a significant decrease (p < 0.05) in the (35)Cl(-) chemical shift at higher ionic strength. Line widths at half-height were significantly (p < 0.05) less for Co(II)/gly than for Co(2+)((aq)) at rho values in the range 0.066-0.40. Intracellular chloride was clearly detectable by (35)Cl NMR spectroscopy in human skin fibroblast cells suspended in medium containing 40 mM Co(II)/gly SR. We determined that, although Co(2+)((aq)) provides a larger shift than Co(II)/gly at the same rho value, there are significant advantages for using Co(II)/gly, such as pH stability, ionic strength independent chemical shifts, narrow (35)Cl(-) NMR resonances, and reduced cellular toxicity, as a SR in biological systems.     

Reactivity of 4‐phenylthiazoles in ruthenium catalyzed direct arylations

The reactivity of the phenyl substituent of 4‐phenylthiazoles in Ru‐catalyzed direct arylation was studied. 4‐Phenylthiazole was found to be unreactive; whereas, the introduction of an aryl unit at C5‐position of 4‐phenylthiazole enhances its reactivity, allowing the selective mono‐arylation of the phenyl unit of 4‐phenylthiazoles in moderate to high yields using 5 mol% of [Ru(p‐cymene)Cl₂]₂ catalyst precursor associated to KOPiv as base. These results reveal that the conformation and electronic properties of 4‐phenylthiazoles are crucial to allow the formation of suitable intermediates in the course of the catalytic cycle. The reaction tolerated both electron‐rich and electron‐poor aryl bromides allowing the straightforward tuning of the electronic properties of the arylated 2‐methyl‐4‐phenyl‐5‐arylthiazoles.     

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.     

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.     

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.