Applying the canonical dual theory in optimal control problems

This paper presents some applications of the canonical dual theory in optimal control problems. The analytic solutions of several nonlinear and nonconvex problems are investigated by global optimizations. It turns out that the backward differential flow defined by the KKT equation may reach the globally optimal solution. The analytic solution to an optimal control problem is obtained via the expression of the co-state. Some examples are illustrated.     

Local discrimination scheme for some unitary operations

It has been shown that for two different multipartite unitary operations U_1 and U_2, when tr(U_1~?U_2) = 0, they can always be perfectly distinguished by local operations and classical communication in the single-run scenario. However, how to find the detailed scheme to complete the local discrimination is still a fascinating problem. In this paper, aiming at some U_1 and U_2 acting on the bipartite and tripartite space respectively, especially for U_1~?U_2 locally unitary equivalent to the high dimensional X-type hermitian unitary matrix V with trV = 0, we put forward the explicit local distinguishing schemes in the single-run scenario.     

A New Eremophilane Sesquiterpenoid from Ligularia przewalskii

Chemistry of Natural Compounds - A new eremophilane sesquiterpenoid, 3β-acetoxy-6α-angeloyloxy-eremophil-1(10),7(11),8(9)-trien-12,8-olide (1), was isolated from Ligularia przewalskii....     

Novel WS2/Fe0.95S1.05 Hierarchical Nanosphere as a Highly Efficient Electrocatalyst for Hydrogen Evolution Reaction

Fe_0.95S_1.05 with high reactivity and stability was incorporated into WS₂ nanosheets via a one-step solvothermal method for the first time. The resulted hybrid catalyst has much higher catalytic activity than WS₂ and Fe_0.95S_1.05 alone, and the optimal WS₂/Fe_0.95S_1.05 hybrid catalyst was found by adjusting the feed ratio. The addition of Fe_0.95S_1.05 was proven to be able to enhance the hydrogen evolution reaction (HER) activity of WS₂, and vice versa. At the same time, it was found that the catalytic effect of the hybrid catalyst was the best when the feed ratio was W : Fe=2 : 1. In other words, we confirmed that there is a synergistic effect between W- and Fe-based sulfide hybrid catalysts, and validated that the reason for the improved HER performance is the strong interaction between the two in the middle sulfur. WS₂/Fe_0.95S_1.05-2 hybrid catalyst leads to enhanced HER activity, which shows a low overpotential of ∼0.172 V at 10 mA cm⁻², low Tafel slope of ∼53.47 mV/decade. This study supplies innovative synthesis of a highly active WS₂/Fe_0.95S_1.05 hybrid catalyst for HER.     

Partial Hydrolysis of Cyanide Coordination Polymers Induced by a Pillar Ligand with Optimized Electrochemical Kinetics for Rechargeable Alkaline Batteries

Coordination polymers are promising cathode materials for rechargeable alkaline batteries. Therefore, the precise modulation of these cathodes by chemical structure and in-depth structure transform study is necessary. Here, two model coordination polymer battery cathodes were designed to demonstrate the dynamic structure–performance relationship. We studied the electrochemical performance of two kinds of nickel-based coordination polymer, comprising a planar 2D cyanide-bridged network and a 3D cyanide-bridged network pillared by pyrazine molecules. The 2D coordination polymer showed serious voltage degradation with poor rate capability, whereas the 3D coordination polymer exhibited stable voltage output coupled with high rate at various current densities. The investigation revealed the underlining relationship of plateau voltage degradation and hydrolysis process of electrodes. It was revealed that the pyrazine pillar molecules in the 3D coordination polymer could suppress the hydrolysis and lead to the in situ formation of partially hydrolyzed structure with excellent electrochemical kinetics; this exhibited obvious smaller peak separation (27 mV compared with 149 mV) and hence an almost twofold increase in capacity retention (31.9 to 50.0 %) and energy density retention (18.2 to 35.9 %) at 10 A g⁻¹.     

A Convenient and Effective Synthesis of Tris-Bridged Tricationic Azolophanes

Two new macrobicyclic imidazolium and benzimidazolium phanes were synthesized by direct quaternization of the corresponding tripodal azacycles with tribromide under high dilution condition in excellent yields. The cyclophanes were identified by ¹H-NMR, ¹³C-NMR, FAB-MS, IR, elemental analysis and X-ray diffraction analysis.     

Effects of structural properties of silicon carbide-derived carbons on their electrochemical double-layer capacitance in aqueous and organic electrolytes

High surface area silicon carbide-derived carbons (Si-CDCs) synthesized by chlorination of beta silicon carbide (βSiC) with two different particle sizes (6 μm and 50 nm) show different porosities with graphitic structure. Transmission electron microscopy, Raman spectroscopy and argon (Ar) and carbon dioxide (CO₂) sorption analyses are used to examine the textural properties of the Si-CDCs. The results show that the particle size of the precursor affects the surface area and porosity of carbons. Furthermore, an additional heat treatment of the Si-CDC with 50-nm particle size for 24 h at 1,000 °C results in a collapse of the pore structure and reduces the surface area. The capacitive behaviours are investigated in H₂SO₄ and in tetraethyl ammonium tetrafluoroborate (TEABF₄)/acetonitrile (AN). The electrochemical performance of the Si-CDCs is influenced by the particle size, surface area, pore volume and pore size distribution. The Si-CDCs exhibit capacitances in 1 M H₂SO₄ of up to 179 F g^?1 and very stable charge–discharge performance over 5,000 cycles. This study shows the crucial importance of ultramicropores less than 1 nm combined with nanosized particles for achieving high capacitance in aqueous electrolyte. Moreover, the graphitic degree at the surface of the Si-CDCs enhances considerably the rate capability and stability in both electrolytes.