Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

Quantum Watermark Algorithm Based on Maximum Pixel Difference and Tent Map

International Journal of Theoretical Physics - A new quantum watermark algorithm is presented by combining maximum pixel difference partitioning with the least significant bit substitution...     

Formation of Azulene-Embedded Nanographene: Naphthalene to Azulene Rearrangement During the Scholl Reaction

Incorporation of a non-hexagonal ring into a nanographene framework can lead to new electronic properties. During the attempted synthesis of naphthalene-bridged double [6]helicene and heptagon-containing nanographene by the Scholl reaction, an unexpected azulene-embedded nanographene and its triflyloxylated product were obtained, as confirmed by X-ray crystallographic analysis and 2D NMR spectroscopy. A 5/7/7/5 ring-fused substructure containing two formal azulene units is formed, but only one of them shows an azulene-like electronic structure. The formation of this unique structure is explained by arenium ion mediated 1,2-phenyl migration and a naphthalene to azulene rearrangement reaction according to an in-silico study. This report represents the first experimental example of the thermodynamically unfavorable naphthalene to azulene rearrangement and may lead to new azulene-based molecular materials.     

Highly dispersed palladium nanoclusters incorporated in amino‐functionalized silica spheres for the selective hydrogenation of succinic acid to γ‐butyrolactone

Highly dispersed palladium nanoclusters incorporated on amino‐functionalized silica sphere surfaces (Pd/SiO₂‐NH₂) were fabricated by a simple one‐pot synthesis utilizing 3‐(2‐aminoethylamino)propyltrimethoxysilane (AAPTS) as coordinating agent. Uniform palladium nanoclusters with an average size of 1.1 nm can be obtained during the co‐condensation of tetraethyl orthosilicate and AAPTS owing to the strong interaction between palladium species and amino groups in AAPTS. The palladium particle size can be controlled by addition of AAPTS and plays a significant role in the catalytic performance. The Pd/SiO₂‐NH₂ catalyst exhibits high catalytic activity for succinic acid hydrogenation with 100% conversion and 94% selectivity towards γ‐butyrolactone using 1,4‐dioxane as solvent at 240°C and 60 bar for 4 h. Moreover, the Pd/SiO₂‐NH₂ catalyst is robust and readily reusable without loss of its catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd.