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.     

Single Crystal to Single Crystal (SC‐to‐SC) Transformation from a Nonporous to Porous Metal–Organic Framework and Its Application Potential in Gas Adsorption and Suzuki Coupling Reaction through Postmodification

A new amino‐functionalized strontium–carboxylate‐based metal–organic framework (MOF) has been synthesized that undergoes single crystal to single crystal (SC‐to‐SC) transformation upon desolvation. Both structures have been characterized by single‐crystal X‐ray analysis. The desolvated structure shows an interesting 3D porous structure with pendent ?NH₂ groups inside the pore wall, whereas the solvated compound possesses a nonporous structure with DMF molecules on the metal centers. The amino group was postmodified through Schiff base condensation by pyridine‐2‐carboxaldehyde and palladium was anchored on that site. The modified framework has been utilized for the Suzuki cross‐coupling reaction. The compound shows high activity towards the C?C cross‐coupling reaction with good yields and turnover frequencies. Gas adsorption studies showed that the desolvated compound had permanent porosity and was microporous in nature with a BET surface area of 2052 m² g^?1. The material also possesses good CO₂ (8 wt %) and H₂ (1.87 wt %) adsorption capabilities.     

The High Energy X-ray telescope (HE) onboard the Insight-HXMT astronomy satellite

The Insight-Hard X-ray Modulation Telescope(Insight-HXMT) is a broadband X-ray and γ-ray(1-3000 ke V) astronomy satellite. One of its three main telescopes is the High Energy X-ray telescope(HE). The main detector plane of HE comprises 18 Na I(Tl)/Cs I(Na) phoswich detectors, where Na I(Tl) is used as the primary detector to measure ~ 20-250 ke V photons incident from the field of view(FOV) defined by collimators, and Cs I(Na) is used as the active shielding detector to Na I(Tl) by pulse shape discrimination. Additionally, Cs I(Na) is used as an omnidirectional γ-ray monitor. The HE collimators have a diverse FOV,i.e. 1.1°×5.7°(15 units), 5.7°×5.7°(2 units), and blocked(1 unit). Therefore, the combined FOV of HE is approximately5.7°×5.7°. Each HE detector has a diameter of 190 mm resulting in a total geometrical area of approximately 5100 cm2, and the energy resolution is ~15% at 60 ke V. For each recorded X-ray event by HE, the timing accuracy is less than 10 μs and the deadtime is less than 10 μs. HE is used for observing spectra and temporal variability of X-ray sources in the 20-250 ke V band either by pointing observations for known sources or scanning observations to unveil new sources. Additionally, HE is used for monitoring the γ-ray burst in 0.2-3 Me V band. This paper not only presents the design and performance of HE instruments but also reports results of the on-ground calibration experiments.