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- Zhi-hong Chen, Z.-J. Liu
- 2007

A generalized Courant algebroid structure is defined on the direct sum bundle D(E) +J(E), where D(E) and J(E) are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a… (More)

In this paper, we study Lie Rinehart bialgebras, the algebraic generalization of Lie bialgebroids. More precisely, we analyze the structure of Lie Rinehart bialgebras for crossed products induced by… (More)

- Shiwu Zhang, Z.-J. Liu
- 2007

For a transitive Lie algebroid A on a connected manifold M and its a representation on a vector bundle F, we study the localization map Y^1: H^1(A,F)-> H^1(L_x,F_x), where L_x is the adjoint algebra… (More)

In this paper, we study Lie Rinehart bialgebras over a commutative algebra, the algebraic generalization of Lie algebroids. More precisely, we analyze the structure of action Lie Rinehart bialgebras… (More)

We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the ψ-sum. We… (More)

- X.-J. Hong, M.-J. Ge, X.-M. Zhao, Z.-R. Fen, Z.-J. Liu
- 1983

Abstract A homologous series of 2′-cyano-4′- n-alkylphenyl-4- n-alkylbiphenylcarboxylates and 4- n-alkylcyclohexyl-p-benzoates were synthesized by treating 2′-cyano-4′-n-alkyl substituted phenols… (More)

- Z.-J. Liu, Zai Yu Chen
- 2019

- Z.-J. Liu, You Gen Shen
- 2004

Abstract The normal grain growth kinetics in two-phase nanostructured films consisting of nanocrystallites embedded in an amorphous matrix is studied by Monte Carlo simulations based on a modified… (More)

- Z.-J. Liu
- ISSAC
- 1990

1. Solving algebraic equations is desired for many problems appeared in the applied science. Sometimes, finding all isolated solutions is enough. Suppose a set of polynomials(abbr. polset), denoted… (More)

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