BACKGROUND Colorectal neuroendocrine neoplasms(NENs)are a rare malignancy that primarily arises from the diffuse distribution of neuroendocrine cells in the colon and rectum.Previous studies have pointed out that the ...BACKGROUND Colorectal neuroendocrine neoplasms(NENs)are a rare malignancy that primarily arises from the diffuse distribution of neuroendocrine cells in the colon and rectum.Previous studies have pointed out that the status of lymph node may be used to predict the prognosis.AIM To investigate the predictive values of lymph node ratio(LNR),positive lymph node(PLN),and log odds of PLNs(LODDS)staging systems on the prognosis of colorectal NENs treated surgically,and compare their predictive values.METHODS This cohort study included 895 patients with colorectal NENs treated surgically from the Surveillance,Epidemiology,and End Results database.The endpoint was mortality of patients with colorectal NENs treated surgically.X-tile software was utilized to identify most suitable thresholds for categorizing the LNR,PLN,and LODDS.Participants were selected in a random manner to form training and testing sets.The prognosis of surgically treating colorectal NENs was examined using multivariate cox analysis to assess the associations of LNR,PLN,and LODDS with the prognosis of colorectal NENs.C-index was used for assessing the predictive effectiveness.We conducted a subgroup analysis to explore the different lymph node staging systems’predictive values.RESULTS After adjusting all confounding factors,PLN,LNR and LODDS staging systems were linked with mortality in patients with colorectal NENs treated surgically(P<0.05).We found that LODDS staging had a higher prognostic value for patients with colorectal NENs treated surgically than PLN and LNR staging systems.Similar results were obtained in the different G staging subgroup analyses.Furthermore,the area under the receiver operating characteristic curve values for LODDS staging system remained consistently higher than those of PLN or LNR,even at the 1-,2-,3-,4-,5-and 6-year follow-up periods.CONCLUSION LNR,PLN,and LODDS were found to significantly predict the prognosis of patients with colorectal NENs treated surgically.展开更多
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
The dynamics of molecular rotational wave packets of D2 induced by ultrashort laser pulses was investigated numerically by solving the time-dependent SchrSdinger equation. Results show that an ultrashort pulse can man...The dynamics of molecular rotational wave packets of D2 induced by ultrashort laser pulses was investigated numerically by solving the time-dependent SchrSdinger equation. Results show that an ultrashort pulse can manipulate a coherent rotational wave packet of D2 se- lectively. In the calculation, a first laser pulse was used to create a coherent rotational wave packet from an initial thermal ensemble of D2 at the temperature of 300 K. The second laser pulse was used to manipulate the rotational wave packet selectively around the first quarter and the three quarters revival. The alignment parameter and its Fourier transform amplitude both illustrate that the relative populations of even and odd rotational states in the final rotational wave packet of D2 can be manipulated by precisely selecting the time delay between the first and the second ultrashort pulse.展开更多
基金Supported by the Zhaoqing Science and Technology Innovation Guidance Project,No.2022040314032.
文摘BACKGROUND Colorectal neuroendocrine neoplasms(NENs)are a rare malignancy that primarily arises from the diffuse distribution of neuroendocrine cells in the colon and rectum.Previous studies have pointed out that the status of lymph node may be used to predict the prognosis.AIM To investigate the predictive values of lymph node ratio(LNR),positive lymph node(PLN),and log odds of PLNs(LODDS)staging systems on the prognosis of colorectal NENs treated surgically,and compare their predictive values.METHODS This cohort study included 895 patients with colorectal NENs treated surgically from the Surveillance,Epidemiology,and End Results database.The endpoint was mortality of patients with colorectal NENs treated surgically.X-tile software was utilized to identify most suitable thresholds for categorizing the LNR,PLN,and LODDS.Participants were selected in a random manner to form training and testing sets.The prognosis of surgically treating colorectal NENs was examined using multivariate cox analysis to assess the associations of LNR,PLN,and LODDS with the prognosis of colorectal NENs.C-index was used for assessing the predictive effectiveness.We conducted a subgroup analysis to explore the different lymph node staging systems’predictive values.RESULTS After adjusting all confounding factors,PLN,LNR and LODDS staging systems were linked with mortality in patients with colorectal NENs treated surgically(P<0.05).We found that LODDS staging had a higher prognostic value for patients with colorectal NENs treated surgically than PLN and LNR staging systems.Similar results were obtained in the different G staging subgroup analyses.Furthermore,the area under the receiver operating characteristic curve values for LODDS staging system remained consistently higher than those of PLN or LNR,even at the 1-,2-,3-,4-,5-and 6-year follow-up periods.CONCLUSION LNR,PLN,and LODDS were found to significantly predict the prognosis of patients with colorectal NENs treated surgically.
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
文摘The dynamics of molecular rotational wave packets of D2 induced by ultrashort laser pulses was investigated numerically by solving the time-dependent SchrSdinger equation. Results show that an ultrashort pulse can manipulate a coherent rotational wave packet of D2 se- lectively. In the calculation, a first laser pulse was used to create a coherent rotational wave packet from an initial thermal ensemble of D2 at the temperature of 300 K. The second laser pulse was used to manipulate the rotational wave packet selectively around the first quarter and the three quarters revival. The alignment parameter and its Fourier transform amplitude both illustrate that the relative populations of even and odd rotational states in the final rotational wave packet of D2 can be manipulated by precisely selecting the time delay between the first and the second ultrashort pulse.
