An efficient synthesis of 4,5-dihydronaphtho[2,1-b]furan through a novel ring transformation of 2H-pyran-2-one

An innovative route for the synthesis of substituted naphtho[2,1-b]furan has been delineated through a ring transformation reaction of suitably functionalized 2H-pyran-2-ones by reaction with 6,7-dihydro-5H-benzofuran-4-one, in good yield.     

Stereoselective electrocatalytic transformation of arylidene- or alkylidenemalononitriles and malonate into alkyl (1R,5R,6R)* 6-substituted 5-cyano-4,4-dialkoxy-2-oxo-3-azabicyclo[3.1.0]hexane-1-carboxylates

Electrolysis of arylidene- or alkylidenemalononitriles and malonate in alcohol in an undivided cell in the presence of sodium halide as mediator results in the stereoselective formation of alkyl (1R,5R,6R)* 6-substituted 5-cyano-4,4-dialkoxy-2-oxo-3-azabicyclo[3.1.0]hexan-1-carboxylates in 50-70% yields.     

Back-and-forth shooting method for solving two-point boundary-value problems

The paper proposes a special iterative method for a nonlinear TPBVP of the form (t)=f(t, x(t),p(t)), (t)=g(t, x(t),p(t)), subject toh(x(0),p(0))=0,e(x(T),p(T))=0. Certain stability properties of the above differential equations are taken into consideration in the method, so that the integration directions associated with these equations respectively are opposite to each other, in contrast with the conventional shooting methods. Via an embedding and a Riccati-type transformation, the TPBVP is reduced to consecutive initial-value problems of ordinary differential equations. A preliminary numerical test is given by a simple example originating in an optimal control problem.     

一个1+1维Boussinesq系统的Darboux变换及其应用

主要考虑1+1维Boussinesq系统的一个Darboux变换,反复利用该Darboux变换,可以从该系统的一个已知解出发,通过代数运算和求导运算得到系统的新解.     

Advances in Electrochemical Decarboxylative Transformation Reactions

Owing to their non-toxic, stable, inexpensive properties, carboxylic acids are considered as environmentally benign alternatives as coupling partners in various organic transformations. Electrochemical mediated decarboxylation of carboxylic acid has emerged as a new and efficient methodology for the construction of carbon-carbon or carbon-heteroatom bonds. Compared with transition-metal catalysis and photoredox catalysis, electro-organic decarboxylative transformations are considered as a green and sustainable protocol due to the absence of chemical oxidants and strong bases. Further, it exhibits good tolerance with various functional groups. In this Minireview, we summarize the recent advances and discoveries on the electrochemical decarboxylative transformations on C−C and C−heteroatoms bond formations.     

High-order rogue waves for the Hirota equation

The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures.     

Modified Kramers formulas for the decay rate in agreement with dynamical modeling

Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.     

MgCu metallic glass

We generate an amorphous MgCu model using the rapid solidification of the melt through a first-principles molecular dynamics approach within a generalised gradient approximation and reveal, for the first time, its structural features and mechanical properties in details. The liquid and glassy MgCu are found to acquire slightly distinct local structures. Yet in both forms of MgCu, most Cu atoms have a tendency to form the ideal and defective icosahedrons while Mg atoms are arranged in complex configurations. The mean coordination number of Cu and Mg at 300 K is 11.31 and 13.73, respectively. The short-range order of MgCu glass is projected to be different than the known crystalline MgCu and Mg₂Cu phases. The mechanical properties of MgCu glass and the CsCl-type MgCu crystal are computed and compared. On the basis of the enthalpy analyses, a possible pressure-induced crystallisation of the MgCu glass into a CsCl-type structure is proposed to occur at around 11 GPa.     

Capacitance and potential coefficients at large distances

The design of capacitive sensors and devices for new and emerging applications would benefit from simple and reliable methods to estimate the capacitance between conductors in terms of the capacitance of the isolated bodies and of the distance between them. The coefficients of potential and capacitance of a pair of conductor are approximated with the first terms of an expansion formula in the inverse of their distance. The form given applies to conductors of generic shapes and position in space. A comparison with the exact value for two spheres shows agreement even for rather small distances.