Exact Solutions Expressible in Rational Formal Hyperbolic and Elliptic Functions for Nonlinear Differential-Difference Equation

A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.     

Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance

For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number- phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenberg equation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coettlcient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.     

Effects of Li Substitution and Sintering Temperature on Properties of Bi0.5（Na,K）0.5TiO3 Lead-Free Piezoelectric Ceramics

Bi0.5 （Na0.72K0.28- x Lix ）0.5 TiO3 （BNKLT- 100x） lead-free piezoelectric ceramics are synthesized by conventional solid state sintering techniques. The dielectric and piezoelectric properties of the BNKLT-100x ceramics as a function of Li content are systematically investigated. It is found that not only Li content but also the sintering temperature has a strong effect on the piezoelectric properties of BNKLT. The piezoelectric constant d33 Of BNKLT varies from 120 to 252pC/N in the Li content range from 0.03 to 0.16. In the sintering temperature range from 1080 to 1130℃, the d33 value of BNKLT-6 changes from 200pC/N to 252pC/N. The BNKLT-6 sample sintered at 1100℃ has the highest piezoelectric constant d33 of 252pC/N, with the electromechanical coupling factors kp of 0.32 and kt of 0.44.     

Synthesis,characterization, and some electrocatalytic properties of heteromultinuclear FeI/RuII Clusters

A series of new heteromultinuclear Fe^I/Ru^II clusters are described. The complexes (η⁶-arene)RuFe₂S₂(CO)₆ (arene = p-cymene 1 , C₆Me₆ 2 ) and Fe₂[μ-S (Cp*Ru)(CO)₂]₂(CO)₆ (Cp* = η⁵-C₅Me₅) ( 3 ) were prepared by the reduction reactions of (μ-S)₂Fe₂(CO)₆ with 2 equiv of LiHBEt₃, followed by treatment (μ-SLi)₂Fe₂(CO)₆ with ruthenium-arene complexes Ru₂(μ-Cl)₂Cl₂(η⁶-arene)₂ or Cp*Ru (CO)₂Cl in 22–33% yields. Further reactions of 1 and 2 with 1 equiv of triphenylphosphine in the presence of the decarbonylating agent Me₃NO·2H₂O, afforded the corresponding monophosphine-substituted Fe^I/Ru^II complexes (η⁶-arene)RuFe₂S₂(CO)₅(Ph₃P) (arene = p-cymene 4 , C₆Me₆ 5 ) in 75% and 78% yields. While treatment of parent complex 1 or 2 with 1 equiv of diphosphine Ph₂PCH₂PPh₂ (dppm) in xylene at reflux temperature resulted in the formation of the diphosphine-bridged RuFe₂S₂(CO)₉ derivate RuFe₂S₂(CO)₇(dppm) ( 6 ). The possible pathway for the formation was proposed. Two isomers of novel macrocyclic complexes involve the (η⁶-arene) Ru-bridged quadruple-butterfly Fe/S clusters [{μ-S (CH₂)₃S-μ}{(μ-CS₂)Fe₂(CO)₆}₂]₂[(η⁶-arene)Ru]₂ (arene = p-cymene 7a and 7b , C₆Me₆ 8a and 8b ) were isolated by reactions of two μ-CS₂-containing dianion [{μ-S (CH₂)₃S-μ}{(μ-S=CS)Fe₂(CO)₆}₂]²⁻ with [Ru₂(μ-Cl)₂Cl₂(η⁶-arene)₂], in which the propylene groups are attached to two S atoms by ee and ea types of bonds respectively. All the new complexes 1 – 8 have been characterized by elemental analysis, spectroscopy, and particularly for 1 – 6 , 7b and 8a by X-ray crystallography. In addition, the electrochemical properties of representative complexes 1 – 4 and 6 have been investigated.     

In situ decoration of CoP/Ti3C2Tx composite as efficient electrocatalyst for Li-oxygen battery

Application of Li-oxygen (Li-O₂) battery is in urgent need of bifunctional ORR/OER electrocatalyst. A surface-functionalization CoP/Ti₃C₂T_x composite was fabricated theoretically, with the optimized electronic structure and more active electron, which is beneficial to the electrochemical reaction. The accordion shaped Ti₃C₂T_x is featured with large specific surface area and outstanding electronic conductivity, which is beneficial for the adequate exposure of active sites and the deposition of Li₂O₂. Transition metal phosphides provide more electrocatalytic active sites and present good electrocatalytic effect. The CoP/Ti₃C₂T_x composite served as the electrocatalyst of Li-O₂ battery reaches a high specific discharge capacity of 17,413 mAh/g at 100 mA/g and the lower overpotential of 1.25 V, superior to those of the CoP and Ti₃C₂T_x individually. The composite of transition metal phosphides and MXene are applied in Li-O₂ battery, not only demonstrating higher cycling stability of the prepared CoP/Ti₃C₂T_x composite, but pointing out the direction for their electrochemical performance improvement.     

Crystal and molecular structure of two new Schiff bases: Paeonol-ethylenediamine and paeonol-1,3-propylenediamine

Two new Schiff bases were prepared by the condensation reaction of paeonol with ethylenediamine (for compound 1) and 1,3-propylenediamine (for compound 2). The compounds were studied with single crystal X-ray diffraction method. Compound 1 is monoclinic, space group P2₁/c, a = 10.956(15) Å, b = 6.767(10) Å, c = 12.494(18) Å; β = 104.66(2)°, V = 896(2) ų, Z = 2. Compound 2 is triclinic, space group P-1, a = 6.878(2) Å, b = 12.141(4) Å, c = 12.414(4) Å; α = 101.023(6)°, β = 103.415(6)°, γ = 102.337(6)°, V = 952.8(6) ų, Z = 2. The molecular structures of 1 and 2 are similar; the molecule being centrosymmetric in 1 but asymmetric in 2.     

Permeation properties to hydrocarbons,perfluorocarbons and chlorofluorocarbons of cross-linked membranes of polymethacrylates with poly(ethylene oxide) and perfluorononyl moieties

Two kinds of cross-linked polymer membranes were prepared by photo polymerization. One of them (PEO membrane) is a co-polymer of methoxy-terminated poly(ethylene glycol) methacrylate (MEMA) and poly(ethylene glycol) dimethacrylate (EDMA) in feed ratio of 70/30 in wt%. The other (PF/PEO membrane) is a co-polymer of 1H,1H,9H-hexadecafluorononyl methacrylate and EDMA in feed ratio of 70/30 in wt%. The block lengths of poly(ethylene oxide) (PEO) are 9 and 14 for MEMA and EDMA, respectively. Permeation properties of inorganic gases, hydrocarbons, perfluorocarbons and chlorofluorocarbons (CFCs) were investigated for these membranes compared with a silicone rubber (SR) membrane. The PF/PEO membrane is inferior to the SR membrane as for CFCs/N₂ separation because the former has lower permeabilities. The PEO membrane has good performance for separation of hydrocarbons and CFCs from N₂ or perfluorocarbons.     

New Exact Solutions for a Class of Nonlinear Coupled Differential Equations

More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.     

Travelling solitary wave solutions to a compound KdV-Burgers equation

Explicit travelling solitary wave solutions to a compound KdV-Burgers equation are obtained by using an automated method. A two-dimensional generalization is discussed.