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...     

A smooth homotopy method for incomplete markets

Mathematical Programming - In the general equilibrium with incomplete asset markets (GEI) model, the excess demand functions are typically not continuous at the prices for which the assets have...     

On s-hamiltonian line graphs of claw-free graphs

For an integer $s\ge 0$, a graph $G$ is $s$-hamiltonian if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian, and $G$ is $s$-hamiltonian connected if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian connected. Thomassen in 1984 conjectured that every 4-connected line graph is hamiltonian (see Thomassen, 1986), and Ku?zel and Xiong in 2004 conjectured that every 4-connected line graph is hamiltonian connected (see Ryjá?ek and Vrána, 2011). In Broersma and Veldman (1987), Broersma and Veldman raised the characterization problem of $s$-hamiltonian line graphs. In Lai and Shao (2013), it is conjectured that for $s\ge 2$, a line graph $L\left(G\right)$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected. In this paper we prove the following.(i) For an integer $s\ge 2$, the line graph $L\left(G\right)$ of a claw-free graph $G$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected.(ii) The line graph $L\left(G\right)$ of a claw-free graph $G$ is 1-hamiltonian connected if and only if $L\left(G\right)$ is 4-connected.     

Strategies for synthesizing non-bioaccumulable alternatives to PFOA and PFOS

This minireview describes the strategies for synthesis of fiuorinated surfactants potentially nonbioaccumulable.Various strategies have been focused on(Ⅰ) reducing the length of the perfluorocarbon chain,(Ⅱ) introducing hetero atoms into the fluorocarbon chain,(Ⅲ) introducing branch(herein and after branch means the fluoro-carbon chain section is not straight).In most cases,the surface tensions versus the surfactant concentrations have been assessed.These above strategies led to various highly fiuorinated(perfluorinated or not perfluorinated) surfactants whose chemical changes enabled to obtain novel alternatives to perfluorooctanoic acid(PFOA) and perfluorooctane sulphonate(PFOS).     

Synthesis and Photophysical Properties of a Sc3N@C80‐Corrole Electron Donor–Acceptor Conjugate

Embedding endohdedral metallofullerenes (EMFs) into electron donor–acceptor systems is still a challenging task owing to their limited quantities and their still largely unexplored chemical properties. In this study, we have performed a 1,3‐dipolar cycloaddition reaction of a corrole‐based precursor with Sc₃N@C₈₀ to regioselectively form a [5,6]‐adduct ( 1 ). The successful attachment of the corrole moiety was confirmed by mass spectrometry. In the electronic ground state, absorption spectra suggest sizeable electronic communications between the electron acceptor and the electron donor. Moreover, the addition pattern occurring at a [5,6]‐bond junction is firmly proven by NMR spectroscopy and electrochemical investigations performed with 1 . In the electronically excited state, which is probed in photophysical assays with 1 , a fast electron‐transfer yields the radical ion pair state consisting of the one‐electron‐reduced Sc₃N@C₈₀ and of the one‐electron‐oxidized corrole upon its exclusive photoexcitation. As such, our results shed new light on the practical work utilizing EMFs as building blocks in photovoltaics.