We prove scattering for the defocusing fourth-order Schrödinger equation in low spatial dimensions (1 n 4). Inspired by the method in (Pausader 2010 Indiana Univ. Math. J. 59 791-822), we utilize a strategy from Kenig and Merle (2006 Invent. Math. 166 645-75) to compensate for the absence of a Morawetz-type estimate, then we use a new virial-type ingredient to finish the proof.

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In this study, paclitaxel (PTX)-loaded polyamidoamin-alkali blue (PTX-P-AB) was prepared in order to investigate the intralymphatic targeting ability and anti-cancer effect after subcutaneous (s.c.) administration. The physicochemical properties and in vitro drug release were evaluated. The lymphatic drainage and lymph nodes (LNs) uptake were examined by pharmacokinetics and distribution recovery of PTX in plasma, LNs, injection site (IS) and tissues after s.c. injection in healthy mice and in tumor-bearing mice. The osmotic pressure of PTX-P-AB affecting the lymphatic targeting was studied. The anti-tumor activity of PTX-P-AB was investigated in mice bearing S180 metastatic tumors. Results showed that PTX-P-AB with suitable and stable physicochemical properties could be used for in vivo lymphatic studies, and displayed the more rapid lymphatic absorption, the higher AUC value in LNs, the longer LNs residence time and the higher metastasis-inhibiting rate compared with Taxol Õ . Enhanced lymphatic drainage from the IS and uptake into lymph by increasing the osmotic pressure of PTX-P-AB indicated that PTX-P-AB possesses the double function of lymphatic tracing and lymphatic targeting, and suggested the potential for the development of lymphatic targeting vectors and the lymphatic tracer for treatment and diagnosis. KeywordsLymphatic drainage and uptake, lymphatic targeting, polyamidoamin-alkali blue, osmotic pressure, subcutaneous administration History

In this study, a novel lymphatic tracer polyamidoamin-alkali blue (PAMAM-AB) was synthesized in order to evaluate the intra-lymphatic targeting ability and lymphatic tropism of PAMAM-AB after subcutaneous administration. UV-Vis, FT-IR, NMR and HPLC characterization were performed to prove the successful synthesis of PAMAM-AB. The calculated AB payload of PAMAM-AB conjugate was seven per dendrimer molecule (27.16% by weight). Hydrolysis stability of PAMAM-AB in vitro was evaluated, which was stable in PBS and human plasma. Lymphatic tracing were studied to determine the blue-stained intensity of PAMAM-AB in right popliteral lymph nodes (PLNs), iliac lymph nodes (ILNs) and para-aortic lymph nodes (PALNs) after subcutaneous administration. The pharmacokinetics and biodistribution of PAMAM-AB in mice were investigated. PLNs, ILNs and PALNs could be obviously blue-stained within 10 min after PAMAM-AB administration, and displayed a more rapid lymphatic absorption, a higher AUC value in lymph nodes and a longer lymph nodes residence time compared with methylene blue solution (MB-S), MB water-in-oil microemulsion (MB-ME), MB multiple microemulsion (MB-MME). Enhanced lymphatic drainage from the injection site and uptake into lymph of PAMAM-AB indicated that PAMAM-AB possesses the double function of lymphatic tracing and lymphatic targeting, and suggested the potential for the development of lymphatic targeting vectors or as a lymphatic tracer in its own right.

In this paper, we give a new proof of the scattering and blow-up theory of the two coupled nonlinear Schrödinger system via establishing the corresponding interaction Morawetz estimate and scattering criterion. The method of this paper simplifies the proof in Xu, and the result of the paper improves the result in Xu. KEYWORDS blowup, coupled NLS system, Morawetz estimate, scattering MSC CLASSIFICATION 35L70; 35Q55