Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.

Using inequality techniques and fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values of λ > 0 and μ > 0 for a fourth order impulsive integral boundary value problem with one-dimensional m-Laplacian and deviating arguments. We discuss our problems under two cases when the deviating arguments are delayed and advanced. Moreover, the nonexistence of a positive solution is also studied. In this paper, our results cover fourth order boundary value problems without deviating arguments and impulsive effect and are compared with some recent results by Jankowski.Keywords: multi-parameter; impulsive integral boundary value problems with advanced and delayed arguments; inequality techniques and fixed point theories; one-dimensional m-Laplacian; existence and nonexistence of positive solutions

Discoveries of tetraquarks not only enrich the hadronic spectrum but also provide more platforms to understand quantum chromodynamics. We study the production processes of hidden-charm and open-charm tetraquarks in B decays by analyzing their topological amplitudes. Relations between different channels are found, which confront tests by experiments to probe the nature of the tetraquarks. Furthermore, promising channels to find more tetraquarks are proposed.

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