Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions [PDF]
Fractal and Fractional, 2020 This work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level.
L. K. Mork +3 more
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Hydrogels Under Superchaotropic Control: Polyoxometalate Stabilization and pH-Responsive Crosslinking in Cellulose Ether Solutions. [PDF]
Angew Chem Int Ed EnglSuperchaotropic binding of Keggin polyoxometalates (POMs) to non‐ionic biopolymers like cellulose ethers (CEs) stabilizes otherwise hydrolytically unstable POMs in aqueous solution and allows conversion of pH‐nonresponsive polymers into pH‐responsive soft materials. The pH‐driven conversion from plenary to lacunary POMs switches superchaotropic binding
Lokare VB +3 more
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On Modulated Lacunary Statistical Convergence of Double Sequences
Mathematics, 2023 In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function).
María del Pilar Romero de la Rosa
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Spatial distribution of 6s<sup>2</sup> lone electron pair in Pb<sub>4</sub>Na(PO<sub>4</sub>)<sub>3</sub> and stereochemical activity of the 6s<sup>2</sup> electron cloud in lead-bearing apatites. [PDF]
Acta Crystallogr B Struct Sci Cryst Eng MaterIn lacunary apatite structure‐type Pb4Na(PO4)3, residual density attributable to the deformed 6s2 electron cloud is found in the vicinity of A2‐site Pb2+ on regular A2 triangle normal to c. Systematic comparison on the size of the A2 triangle with other apatite‐type compounds indicates limited stereochemical activity of the orbital.Single crystals of ...
Hirano K, Okudera H.
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More Than a Buffer in Biochemistry: Tris as an Architect and Gatekeeper of Metal-Oxo Assembly. [PDF]
Angew Chem Int Ed EnglTris(hydroxymethyl)aminomethane, depicted as an octopus, acts as an alkoxy ligand, chelator, and structure‐directing buffer that programs polyoxometalate's speciation, nucleation, and heterometal insertion in aqueous solution. ABSTRACT Polyoxometalates (POMs, molecular metal–oxo clusters) are typically studied and applied in aqueous media, where ...
Gumerova NI, Rompel A.
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In Situ Observation of Polyoxometalate Formation by Vibrational Spectroscopy. [PDF]
ChemistryIn‐situ IR and Raman spectroscopy were employed to observe the formation of polyoxometalates (POMs) in aqueous solution. Thereby key intermediates were identified, and better understanding of POM formation enabled the development of an improved method for the synthesis of vanadium‐substituted phosphomolybdates, which are important catalysts for ...
Krueger JH +5 more
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Centered Polygonal Lacunary Sequences
Mathematics, 2019 Lacunary functions based on centered polygonal numbers have interesting features which are distinct from general lacunary functions. These features include rotational symmetry of the modulus of the functions and a notion of polished level sets.
Keith Sullivan +2 more
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Axioms, 2018 In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical ...
Ömer Kişi +2 more
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Invariant means and lacunary sequence spaces of order (α, β)
Demonstratio MathematicaIn this article, we use the notion of lacunary statistical convergence of order (α,β)\left(\alpha ,\beta ) to introduce new sequence spaces by lacunary sequence, invariant means defined by Musielak-Orlicz function ℳ=(ℵk){\mathcal{ {\mathcal M} }}=\left({\
Ayman-Mursaleen Mohammad +3 more
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Critical zeros of lacunary $L$-functions [PDF]
Acta Arithmetica, 2020 49 ...
Conrey, J B, Iwaniec, H
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