In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum p μ with its alternative p μ + mωβf μ (x μ ). In particular, the quantum dynamics is considered for the function f μ (x μ ) to be taken as cornell potential, exponential-type potentialand singular potential. For cornell potential and exponential-type potential, the corresponding radial equations can be mapped into the confluent hypergeometric equation and hypergeometric equation separately. The corresponding eigenfunctions can be represented as confluent hypergeometric function and hypergeometric function.The equations satisfed by the exact energy spectrum have been found. For singular potential, the wave function and energy eigenvalue are given exactly by power series method.

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Background: Thymomas (Ts) and thymic carcinomas (TCs) are rare primary tumors of the mediastinum. Paraneoplastic syndrome (PNS) is an important feature of thymoma, which presents great challenges to clinicians.Methods: The present study uses the weighted gene co-expression network analysis (WGCNA) to identify possible immunologic mechanisms of thymoma. RNA sequencing data from thymoma samples were downloaded from the TCGA. Core genes were taken from the module that is closely related to the WHO’s stage of classification. Enhanced analysis using the online database “Metascape” and an overall survival (OS) analysis were carried out via the Kaplan–Meier method. The hub genes were obtained from the protein–protein interaction (PPI) network. In addition, we jointly analyzed multiple sets of PNS data related to thymomas from other sources to verify the correlation between thymomas and PNS. The impact of hub genes on the prognosis of PNS was evaluated via the ROC curve, with simultaneous analysis of immune infiltration by CIBERSORT.Findings: The 14 immune hub genes closely related to thymomas were found to be jointly involved in the T-cell receptor signaling pathway. Compared to the normal thymus and type B1/B2 thymoma, there is a lower number of T-cells in type A/B3 thymoma and thymic carcinoma. The expression of genes related to the T-cell receptor signaling pathway appeared defective. The low expression of CD247 and the decrease in the number of mature T-cells are common features among thymomas, specific pulmonary fibrosis, rheumatoid arthritis, and systemic lupus erythematosus.

The one-dimensional Dirac equation is studied for square-well potential in the presence of generalized uncertainty principle (GUP). Based on the exact solution, the general and explicit relation between the phase time and the dwell time is given and quantified. The phase time, dwell time and self-interference delay are calculated as well and it is shown that the GUP has effects on the tunneling time. Moreover, the effect of GUP on the tunneling time showed a slight change with the change of mass, and goes to zero with the increase of kinetic energy.

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