The n-fold Darboux transform (DT) is a 2×2 matrix for the Ablowitz-Kaup-NewellSegur (AKNS) system. In this paper, each element of this matrix is expressed by 2n + 1 ranks' determinants. Using these formulae, the determinant expressions of eigenfunctions generated by the n-fold DT are obtained. Furthermore, we give out the explicit forms of the n-soliton surface of the Nonlinear Schrodinger Equation (NLS) by the determinant of eigenfunctions.

The effect of post-space treatment on the retention of fiber posts in different root regions was evaluated using two self-etching systems. Post spaces were prepared in extracted premolars and then the root canals were subjected to one of the following post-space treatments: (i) water irrigation (control); (ii) etching with 35% phosphoric acid for 30 s; (iii) irrigation with 17% EDTA followed by 5.25% sodium hypochlorite (NaOCl); and (iv) ultrasonic agitation associated with 17% EDTA and 5.25% NaOCl irrigating solutions. The dentin surfaces were examined under scanning electron microscopy (SEM) after different post-space treatments. Fiber posts were then luted in the treated roots using resin cement with either Clearfil SE Bond or Clearfil DC Bond, and the thin-slice push-out test was performed. Scanning electron microscopy showed that all the post-space treatments tested were effective in removal of the smear layer of debris, or sealer/gutta-percha remnants, on the root canal. The apical push-out strength was affected by post-space treatment. Both 35% phosphoric acid etching and ultrasonic agitation in combination with EDTA/NaOCl irrigation improved the apical push-out strength of the fiber post, regardless of the type of self-etching system. A solo irrigation with an EDTA/NaOCl solution resulted in a lower apical push-out strength compared with the other two experimental groups.

No abstract

Highly enantioselective [3+ +3] and [3+ +4] annulations of isatin-derived enals with ethynylethylene carbonates and ethynyl benzoxazinanones are enabled by NHC/cooper cooperative catalysis,leading to abig library of spirooxindole derivatives in high structural diversity and enantioselectivity (up to 99 %e e). Both reactions represent an icely synergistic integration of NHC and copper catalysis,i nw hichb oth catalysts activate the substrates and the chiral NHC perfectly controls the stereochemistry.The 3,3'-spirocyclicoxindole unit is aprivileged heterocyclic moiety that is prevalent in ag reat number of biologically active natural products and pharmaceutical molecules. [1] Consequently,t he catalytic enantioselective construction of the spirooxindole skeleton with an all-carbon quaternary stereogenic center at the C3-position has received longstanding interest, but still remains asignificant challenge in organic synthesis. [2] In the past two decades,t he chemistry of Nheterocyclic carbenes (NHCs) has witnessed significant development in terms of stereoselective synthesis,a nd now provides apowerful approach to build molecular complexity, primarily through polarity-reversal approaches. [3] In particular, studies on the homoenolate species generated by NHC catalysis have gained widespread popularity in recent years. [3c, f] In 2016, the Enders group successfully established an NHC-catalyzed asymmetric [3+ +4] cyclization of isatinderived enals with in situ generated aza-o-quinone methides, azoalkenes,and nitrosoalkenes,which proceeds though NHCbased three-carbon homoenolates,l eading to as eries of highly enantioenriched spirooxindoles (Scheme 1a). [4] Since then, an umber of methods have been developed to access 3,3'-spirocyclic oxindole skeletons through NHC-catalyzed [3 + n]annulations of isatin-derived enals [5] by using asimilar concept. [6] Recently,c ooperative catalysis between metals and Nheterocyclic carbenes (NHCs) has greatly enhanced the synthetic repertoire of carbene catalysis. [7] Activation modes accessible through cooperative catalysis have resulted in remarkable improvements in reactivity,e fficiency,a nd selectivity for as eries of new enantioselective transformations. NHCs are routinely used as strongly coordinating ligands due to their strong propensity for binding to transition metals with high affinity. [8] As such, the combination of these nucleophilic organocatalysts with transition metals [9] typically leads to the deactivation of either or both of the two catalysts.B yn ow, several groups have figured out solutions to such problems through careful evaluations of catalytic systems,a nd the combination of NHCs with palladium, [10] ruthenium, [11] and copper [12] catalysts has enabled av ariety of unprecedented asymmetric reactions (Scheme 1b). Remarkably,s everal pioneering reports from Scheidt, [10a] Liu, [10b,c] and co-workers have demonstrated synergy between NHC and p-allylpalladium in catalysis.Since then, cooperative catalysis with NHC and palladium, as reported by Glorius and c...