Cauchy-Poisson Problem for a Two-layer Fluid with an Inertial Surface

This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.

Effect of music therapy derived from the five elements in Traditional Chinese Medicine on post-stroke depression

OBJECTIVE: To evaluate the clinical efficacy and safety of five phase music therapy in patients with depression after ischemic stroke.METHODS: A total of 92 patients with post-stroke depression were randomly divided into the control group(32 cases), treatment group A(30 cases), and treatment group B(30 cases). All groups were given basic therapies for cerebral infarction. In addition,the control group was administerd 50 mg of oral sertraline hydrochloride daily, while treatment groups A and B received needling at Baihui(GV 20)plus acupoint injection at Yanglingquan(GB 34) daily; treatment group B also received music therapy derived from the five phases in Traditional ChineseMedicine theory twice daily. All treatments were administered for 5 d per treatment cycle for three cycles, with a 1 d interval between cycles. In all three groups, Hamilton's depression scale(HAMD-17)score and the activities of daily life(ADL) score were measured before and after treatment, and side effects were assessed with the treatment emergent symptom scale.RESULTS: The HAMD-17 score significantly decreased after treatment in all three groups, and the post-treatment reduction in HAMD-17 score was markedly greater in treatment group B than in treatment group A(P < 0.01). The ADL score significantly increased after treatment in all three groups,and the post-treatment increase in ADL score was significantly greater in treatment group B than in treatment group A(P < 0.01). The treatment emergent symptom scale score was highest in the control group, and lowest in group B, and significantly differed between the three groups(P < 0.01).CONCLUSION: Five phase music therapy plus acupoint needling and acupoint injection can improve the symptoms in patients with post-stroke depression.