Synthesis of 3-substituted 2-cyclohexenones through umpoled functionalization

A new protocol to obtain 3-substituted 2-cyclohexenones, was developed by reversing the chemical reactivity of 2-cyclohexenone. One-pot synthesis of 3-substituted 2-cyclohexenones can be achieved by treatment of 3-phenylthiosilyl enol ether with a mixture of t-BuLi/HMPA that allows hydrogen-selective exchange in presence of reactive electrophiles such as aldehydes, ketones and alkyl halides. This affords the corresponding product in moderate overall yield, after silyl enol ether cleavage and concomitant thiophenol elimination initiated with TBAF.     

Cobalt-catalyzed regioselective [3+2] annulation of ortho-formyl and acetyl substituted phenylboronic acids with alkynes

Treatment of alkynes with ortho-formyl and acetyl phenylboronic acids in the presence of a cobalt catalyst resulted in the formation of 2,3-disubstituted indenols in good yields. When aryl silyl alkynes were used, 2-aryl-3-silyl indenols were obtained regioselectively in good yields.     

On Rectifiable Curves in the Plane

This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral. Received August 10, 1999, Revised December 27, 1999, Accepted January 14, 2000     

Non-abelian extensions of Lie 2-algebras

In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.     

Strictly nontame primitive elements of the free metabelian Lie algebra of rank 3

We prove that the free metabelian Lie algebra M ₃ of rank 3 over an arbitrary field K admits strictly nontame primitive elements.     

Finite derivation type for large ideals

In this paper we give a partial answer to the following question: does a large subsemigroup of a semigroup S with the finite combinatorial property finite derivation type (FDT) also have the same property? A positive answer is given for large ideals. As a consequence of this statement we prove that, given a finitely presented Rees matrix semigroup M[S;I,J;P], the semigroup S has FDT if and only if so does M[S;I,J;P].     

特征幂零n-Lie代数

研究了一类特殊的幂零n-Lie代数,其所有导子都是幂零的,称其为特征幂零n-Lie代数.本文主要是得到了一般的n-Lie代数是特征幂零n-Lie代数的一些充要条件.     

A class of non-degenerate solvable Lie Algebras and their derivations

The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.     

Nonlinear Jordan Higher Derivations of Triangular Algebras

In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algeb...     

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.