On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved

Some Nonlinear Gronwall-Bellman-Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications

Some Gronwall-Bellman-Gamidov type integral inequalities with power nonlinearity and their weakly singular analogues are established, which can give the explicit bound on solution of a class of nonlinear fractional integral equations. An example is presented to show the application for the qualitative study of solutions of a fractional integral equation with the Riemann-Liouville fractional operator

Some Nonlinear Gronwall-Bellman-Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications

Some Gronwall-Bellman-Gamidov type integral inequalities with power nonlinearity and their weakly singular analogues are established, which can give the explicit bound on solution of a class of nonlinear fractional integral equations. An example is presented to show the application for the qualitative study of solutions of a fractional integral equation with the Riemann-Liouville fractional operator

TfR1 binding with H-ferritin nanocarrier achieves prognostic diagnosis and enhances the therapeutic efficacy in clinical gastric cancer

H-ferritin (HFn) nanocarrier is emerging as a promising theranostic platform for tumor diagnosis and therapy, which can specifically target tumor cells via binding transferrin receptor 1 (TfR1). This led us to investigate the therapeutic function of TfR1 in GC. The clinical significance of TfR1 was assessed in 178 GC tissues by using a magneto-HFn nanoparticle-based immunohistochemistry method. The therapeutic effects of doxorubicin-loaded HFn nanocarriers (HFn-Dox) were evaluated on TfR1-positive GC patient-derived xenograft (GC-PDX) models. The biological function of TfR1 was investigated through in vitro and in vivo assays. TfR1 was upregulated (73.03%) in GC tissues, and reversely correlated with patient outcome. TfR1-negative sorted cells exhibited tumor-initiating features, which enhanced tumor formation and migration/invasion, whereas TfR1-positive sorted cells showed significant proliferation ability. Knockout of TfR1 in GC cells also enhanced cell invasion. TfR1-deficient cells displayed immune escape by upregulating PD-L1, CXCL9, and CXCL10, when disposed with IFN-γ. Western blot results demonstrated that TfR1-knockout GC cells upregulated Akt and STAT3 signaling. Moreover, in TfR1-positive GC-PDX models, the HFn-Dox group significantly inhibited tumor growth, and increased mouse survival, compared with that of free-Dox group. TfR1 could be a potential prognostic and therapeutic biomarker for GC: (i) TfR1 reversely correlated with patient outcome, and its negative cells possessed tumor-aggressive features; (ii) TfR1-positive cells can be killed by HFn drug nanocarrier. Given the heterogeneity of GC, HFn drug nanocarrier combined with other therapies toward TfR1-negative cells (such as small molecules or immunotherapy) will be a new option for GC treatment