The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been a...The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel an- alytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been ex- tensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenom- ena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.展开更多
Background:Numerous studies have revealed a tight connection between tumor development and the coagulation system.However,the effects of coagulation on the prognosis and tumor microenvironment(TME)of clear cell renal ...Background:Numerous studies have revealed a tight connection between tumor development and the coagulation system.However,the effects of coagulation on the prognosis and tumor microenvironment(TME)of clear cell renal cell carcinoma(ccRCC)remain poorly understood.Methods:We employed the consensus clustering method to characterize distinct molecular subtypes associated with coagulation patterns.Subsequently,we examined variations in the overall survival(OS),genomic profiles,and TME characteristics between these subtypes.To develop a prognostic coagulation-related risk score(CRRS)model,we utilized the least absolute shrinkage and selection operator Cox regression and stepwise multivariate Cox regression analyses.We also created a nomogram to aid in the clinical application of the risk score,evaluating the relationships between the CRRS and the immune microenvironment,responsiveness to immunotherapy,and targeted treatment.The clinical significance of PLAUR and its biological function in ccRCC were also further analyzed.Results:There were significant differences in clinical features,prognostic stratification,genomic variation,and TME characteristics between the two coagulation-related subtypes.We established and validated a CRRS using six coagulation-related genes that can be employed as an effective indicator of risk stratification and prognosis estimation for ccRCC patients.Significant variations in survival outcomes were observed between the high-and low-risk groups.The nomogram was proficient in predicting the 1-,3-,and 5-year OS.Additionally,the CRRS emerged as a novel tool for evaluating the clinical effectiveness of immunotherapy and targeted treatments in ccRCC.Moreover,we confirmed upregulated PLAUR expression in ccRCC samples that was significantly correlated with poor patient prognosis.PLAUR knockdown notably inhibited ccRCC cell proliferation and migration.Conclusion:Our data suggested that CRRS may be employed as a reliable predictive biomarker that can provide therapeutic benefits for immunotherapy and targeted therapy in ccRCC.展开更多
文摘The simplified modified Camassa-Holm (SMCH) equation is an important nonlinear model equation for identifying various wave phenomena in ocean engineering and science. The new auxiliary equation (NAE) method has been applied to the SMCH equation. Base on the method, we have obtained some novel an- alytical solutions such as hyperbolic, trigonometric, exponential, and rational function solutions of the SMCH equation. For appropriate values of parameters, three dimensional (3D) and two dimensional (2D) graphs are designed by Mathematica. The stability of the model is also discussed in this manuscript. The dynamic and physical behaviors of the solutions derived from the SMCH equation have been ex- tensively discussed by these plots. All our solutions are indispensable for understanding the nonlinear phenomena of dispersive waves that are important in ocean engineering and science. In addition, our results are essential to clarify the various oceanographic applications containing ocean gravity waves, offshore rig in water, energy associated with a moving ocean wave and numerous other related phenom- ena. Finally, the obtained solutions are helpful for studying wave interactions in many new structures and high-dimensional models.
文摘Background:Numerous studies have revealed a tight connection between tumor development and the coagulation system.However,the effects of coagulation on the prognosis and tumor microenvironment(TME)of clear cell renal cell carcinoma(ccRCC)remain poorly understood.Methods:We employed the consensus clustering method to characterize distinct molecular subtypes associated with coagulation patterns.Subsequently,we examined variations in the overall survival(OS),genomic profiles,and TME characteristics between these subtypes.To develop a prognostic coagulation-related risk score(CRRS)model,we utilized the least absolute shrinkage and selection operator Cox regression and stepwise multivariate Cox regression analyses.We also created a nomogram to aid in the clinical application of the risk score,evaluating the relationships between the CRRS and the immune microenvironment,responsiveness to immunotherapy,and targeted treatment.The clinical significance of PLAUR and its biological function in ccRCC were also further analyzed.Results:There were significant differences in clinical features,prognostic stratification,genomic variation,and TME characteristics between the two coagulation-related subtypes.We established and validated a CRRS using six coagulation-related genes that can be employed as an effective indicator of risk stratification and prognosis estimation for ccRCC patients.Significant variations in survival outcomes were observed between the high-and low-risk groups.The nomogram was proficient in predicting the 1-,3-,and 5-year OS.Additionally,the CRRS emerged as a novel tool for evaluating the clinical effectiveness of immunotherapy and targeted treatments in ccRCC.Moreover,we confirmed upregulated PLAUR expression in ccRCC samples that was significantly correlated with poor patient prognosis.PLAUR knockdown notably inhibited ccRCC cell proliferation and migration.Conclusion:Our data suggested that CRRS may be employed as a reliable predictive biomarker that can provide therapeutic benefits for immunotherapy and targeted therapy in ccRCC.
