BACKGROUND Ampullary adenocarcinoma is a rare malignant tumor of the gastrointestinal tract.Currently,only a few cases have been reported,resulting in limited information on survival.AIM To develop a dynamic nomogram ...BACKGROUND Ampullary adenocarcinoma is a rare malignant tumor of the gastrointestinal tract.Currently,only a few cases have been reported,resulting in limited information on survival.AIM To develop a dynamic nomogram using internal and external validation to predict survival in patients with ampullary adenocarcinoma.METHODS Data were sourced from the surveillance,epidemiology,and end results stat database.The patients in the database were randomized in a 7:3 ratio into training and validation groups.Using Cox regression univariate and multivariate analyses in the training group,we identified independent risk factors for overall survival and cancer-specific survival to develop the nomogram.The nomogram was validated with a cohort of patients from the First Affiliated Hospital of the Army Medical University.RESULTS For overall and cancer-specific survival,12(sex,age,race,lymph node ratio,tumor size,chemotherapy,surgical modality,T stage,tumor differentiation,brain metastasis,lung metastasis,and extension)and 6(age;surveillance,epidemiology,and end results stage;lymph node ratio;chemotherapy;surgical modality;and tumor differentiation)independent risk factors,respectively,were incorporated into the nomogram.The area under the curve values at 1,3,and 5 years,respectively,were 0.807,0.842,and 0.826 for overall survival and 0.816,0.835,and 0.841 for cancer-specific survival.The internal and external validation cohorts indicated good consistency of the nomogram.CONCLUSION The dynamic nomogram offers robust predictive efficacy for the overall and cancer-specific survival of ampullary adenocarcinoma.展开更多
In this paper,we investigate three types of Feynman integrals up to any loop,including the massless banana integral,the one-mass banana integral,and the massless three-point multi-edge integral.Although these integral...In this paper,we investigate three types of Feynman integrals up to any loop,including the massless banana integral,the one-mass banana integral,and the massless three-point multi-edge integral.Although these integrals are simple in topology,they are involved in many interesting processes,like heavy quarks production and decay,as well as massless quark gluon form factors.By using one-loop integration formulas recursively,we obtain the analytic results at any loop order.It turns out that the results are quite simple and compact.The calculation method used in this work is straightforward,and may be generalized to more general cases.展开更多
In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism ...In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.展开更多
基金Supported by the Appropriate Technology Promotion Program in Chongqing,No.2023jstg005.
文摘BACKGROUND Ampullary adenocarcinoma is a rare malignant tumor of the gastrointestinal tract.Currently,only a few cases have been reported,resulting in limited information on survival.AIM To develop a dynamic nomogram using internal and external validation to predict survival in patients with ampullary adenocarcinoma.METHODS Data were sourced from the surveillance,epidemiology,and end results stat database.The patients in the database were randomized in a 7:3 ratio into training and validation groups.Using Cox regression univariate and multivariate analyses in the training group,we identified independent risk factors for overall survival and cancer-specific survival to develop the nomogram.The nomogram was validated with a cohort of patients from the First Affiliated Hospital of the Army Medical University.RESULTS For overall and cancer-specific survival,12(sex,age,race,lymph node ratio,tumor size,chemotherapy,surgical modality,T stage,tumor differentiation,brain metastasis,lung metastasis,and extension)and 6(age;surveillance,epidemiology,and end results stage;lymph node ratio;chemotherapy;surgical modality;and tumor differentiation)independent risk factors,respectively,were incorporated into the nomogram.The area under the curve values at 1,3,and 5 years,respectively,were 0.807,0.842,and 0.826 for overall survival and 0.816,0.835,and 0.841 for cancer-specific survival.The internal and external validation cohorts indicated good consistency of the nomogram.CONCLUSION The dynamic nomogram offers robust predictive efficacy for the overall and cancer-specific survival of ampullary adenocarcinoma.
基金supported in part by the National Natural Science Foundation of China(NSFC)under Grants Nos.12175048 and 12205061supported by the Guangdong Basic and Applied Basic Research Foundation under Grant No.2022A1515010041.
文摘In this paper,we investigate three types of Feynman integrals up to any loop,including the massless banana integral,the one-mass banana integral,and the massless three-point multi-edge integral.Although these integrals are simple in topology,they are involved in many interesting processes,like heavy quarks production and decay,as well as massless quark gluon form factors.By using one-loop integration formulas recursively,we obtain the analytic results at any loop order.It turns out that the results are quite simple and compact.The calculation method used in this work is straightforward,and may be generalized to more general cases.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1236104012461035)+1 种基金the Outstanding Youth Fund of Gansu Province(Grant No.24JRRA121)the Scientific Research Ability Improvement Program for Young Teachers of Northwest Normal University(Grant No.NWNU-LKQN2021-17)。
文摘In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.
