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...     

Scaling Behavior between Heat Capacity and Thermal Expansion in Solids

We experimentally analyze the heat capacity and thermal expansion of reference solids in a wide temperature range from several Kelvin to melting temperature,and establish a universal double-linear relation between the experimental heat capacity C_p and thermal expansion β,which is different from the previous models.The universal behavior between heat capacity and thermal expansion is important to predict the thermodynamic parameters at constant pressure,and is helpful for understanding the nature of thermal properties in solids.     

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.     

Strain induced strengthening of soft thermoplastic polyurethanes under cyclic deformation

We investigate the cyclic mechanical behavior in uniaxial tension of three different commercial thermoplastic polyurethane elastomers (TPU) often considered as a sustainable replacement for common filled elastomers. All TPU have similar hard segment contents and linear moduli but sensibly different large strain properties as shown by X-ray analysis. Despite these differences, we found a stiffening effect after conditioning in step cyclic loading which greatly differs from the common softening (also referred as Mullins effect) observed in chemically crosslinked filled rubbers. We propose that this self-reinforcement is related to the fragmentation of hard domains, naturally present in TPU, in smaller but more numerous sub-units that may act as new physical crosslinking points. The proposed stiffening mechanism is not dissimilar to the strain-induced crystallization observed in stretched natural rubber, but it presents a persistent nature. In particular, it may cause a local reinforcement where an inhomogeneous strain field is present, as is the case of a crack propagating in cyclic fatigue, providing a potential explanation for the well-known toughness and wear resistance of TPU.