The Shannon-McMillan theorem for ergodic quantum lattice systems

We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstrates the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on -lattices: the entropy gives the logarithm of the essential number of eigenvectors of the system on large boxes. The one-dimensional case covers quantum information sources and is basic for coding theorems.     

Health-Promoting Capacities of In Vitro and Cultivated Goji (Lycium chinense Mill.) Fruit and Leaves; Polyphenols,Antimicrobial Activity,Macro- and Microelements and Heavy Metals

There is a growing interest among the public in fruit with a positive impact on human health. Two goji berry cultivars (‘No. 1’ and ‘New Big’) were propagated in vitro, grown in an orchard and then evaluated for macro- and microelements and harmful heavy metals (i.e., Pb, Ni, and Cd). The leaves and fruit were also assessed for nutritional value, polyphenols and the antimicrobial activity of the leaves. ‘New Big’ was characterized by a higher content of macro elements in the leaves (in vitro and orchard) and a higher content of microelements in the fruit. The harmful substances content was below the minimum value. Furthermore, neither the fruit nor the leaves contained cadmium. This study also indicated that leaves had a higher content of polyphenols compared to the fruit. The fruits were characterized by their health-promoting capacities, while the leaves were characterized by their antibacterial activity. Among the Gram-positive bacteria, the most sensitive strain was Bacillus subtilis, and among the Gram-negative bacteria, it was Proteus vulgaris. Taking into consideration the Recommended Daily Allowance (RDA) for minerals, goji berries can be declared to be a source of Cu, Fe, Mn, Zn and P.     

Phosphorus Vacancies that Boost Electrocatalytic Hydrogen Evolution by Two Orders of Magnitude

Vacancy engineering is an effective strategy to manipulate the electronic structure of electrocatalysts to improve their performance, but few reports focus on phosphorus vacancies (Pv). Herein, the creation of Pv in metal phosphides and investigation of their role in alkaline electrocatalytic hydrogen evolution reaction (HER) is presented. The Pv‐modified catalyst requires a minimum onset potential of 0 mV vs. RHE, a small overpotential of 27.7 mV to achieve 10 mA cm^?2 geometric current density and a Tafel slope of 30.88 mV dec^?1, even outperforms the Pt/C benchmark (32.7 mV@10 mA cm^?2 and 30.90 mV dec^?1). This catalyst also displays superior stability up to 504 hours without any decay. Experimental analysis and density functional theory calculations suggest Pv can weaken the hybridization of Ni 3d and P 2p orbitals, enrich the electron density of Ni and P atoms nearby Pv, and facilitate H* desorption process, contributing to outstanding HER activity and facile kinetics.     

Nitrogen self-doped nanosized TiO2 sheets with exposed {001} facets for enhanced visible-light photocatalytic activity

Nitrogen self-doped TiO(2) nanosheets with exposed {001} facets (ca. 67%) were synthesized by solvothermal treatment of TiN in a HNO(3)-HF ethanol solution and exhibited much higher visible-light photocatalytic H(2)-production activity than nitrogen doped TiO(2) microcrystallites with exposed {001} facets (ca. 60%) by a factor of 4.1.     

Organic acid-assisted soft-templating synthesis of ordered mesoporous carbons

A series of soft-templated ordered mesoporous carbons (OMCs) was synthesized by using resorcinol and formaldehyde as carbon precursors, triblock copolymer Pluronic F127 as a soft-template, and an organic acid (acetic, benzoic, citric, oxalic, or succinic) as a polymerization reaction catalyst. The aforementioned organic acids were strong enough to facilitate the formation of ordered mesophases by the block copolymer template used and to catalyze the polymerization reaction of resorcinol and formaldehyde in this template. The use of weak organic acids instead of strong inorganic acids such as HCl eliminated inorganic anions from the reaction environment and resulted in high surface area OMCs. Basically, the resulting carbons showed the surface areas and pore volumes comparable to those reported for the carbons prepared under similar conditions but in the presence of strong inorganic acids. Electron microscopy analysis proved the presence of ordered mesopores, whereas thermogravimetric analysis showed a good thermal stability of these carbons.