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Some invariant theorems on geometry of Einstein non-symmetric field theory.

Liu, Shu-Lin; Xu, Sen-Lin — 1983

International Journal of Mathematics and Mathematical Sciences

Existence of positive solutions for boundary-value problems with integral boundary conditions and sign changing nonlinearities.

Liu, Shu; Jia, Mei; Tian, Yingqiang — 2010

Electronic Journal of Differential Equations (EJDE) [electronic only]

Chung-Feller property in view of generating functions.

Liu, Shu-Chung; Wang, Yi; Yeh, Yeong-Nan — 2011

The Electronic Journal of Combinatorics [electronic only]

Catalan numbers modulo $2^{k}$ .

Liu, Shu-Chung; Yeh, Jean C.-C. — 2010

Journal of Integer Sequences [electronic only]

Necessary and sufficient conditions for oscillations of delay partial difference equations

Bing Gen Zhang; Shu Tang Liu — 1995

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is concerned with the delay partial difference equation (1) $A_{m + 1, n} + A_{m, n + 1} - A_{m, n} + Σ_{i = 1}^{u} p_{i} A_{m - k_{i}, n - l_{i}} = 0$ where $p_{i}$ are real numbers, $k_{i}$ and $l_{i}$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.

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