In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval...In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.展开更多
BACKGROUND The log odds of positive lymph nodes(LODDS)are correlated with survival outcomes in gastric cancer(GC)patients.However,the prognostic value across different tumor differentiation levels remains unclear.AIM ...BACKGROUND The log odds of positive lymph nodes(LODDS)are correlated with survival outcomes in gastric cancer(GC)patients.However,the prognostic value across different tumor differentiation levels remains unclear.AIM To evaluate the independent prognostic value of LODDS and the stratified predictive efficacy in GC patients with different histologic differentiations.METHODS We conducted a retrospective analysis of 2103 GC patients who underwent radical gastrectomy at Zhejiang Cancer Hospital.The prognostic value of LODDS was compared with that of other lymph node-based metrics,including the pathologic N stage,number of positive lymph nodes,number of total lymph nodes,and lymph node ratio,stratified by tumor differentiation.RESULTS LODDS was identified as an independent prognostic factor for overall survival in moderately to poorly differentiated GC patients.LODDS demonstrated superior predictive accuracy over other lymph node metrics.A nomogram incorporating LODDS,age,carbohydrate antigen(CA)125,carcinoembryonic antigen,and tumor differentiation showed good predictive accuracy(C-index=0.703).A higher LODDS was significantly associated with an increased risk of recurrence or metastasis,poorly differentiated tumors,advanced cancer,mucinous gastric adenocarcinoma,nerve invasion,and vascular tumor thrombus.Additionally,LODDS was positively correlated with the tumor markers CA19-9,CA72-4,CA125,and CA242(all P<0.05).CONCLUSION LODDS is an independent prognostic indicator for patients with moderately and poorly differentiated GC,and its predictive performance is superior to that of other models.展开更多
A triple-band miniaturized end-fire antenna based on the odd modes of spoof surface plasmonic polariton(SSPP)waveguide resonator is proposed in this paper.To meet the ever increasing demand for more communication chan...A triple-band miniaturized end-fire antenna based on the odd modes of spoof surface plasmonic polariton(SSPP)waveguide resonator is proposed in this paper.To meet the ever increasing demand for more communication channels and less antenna sizes,multi-band antennas are currently under intensive investigation.By a novel feeding method,three odd modes are excited on an SSPP waveguide resonator,which performs as an end-fire antenna operating at three bands,7.15-7.26 GHz,11.6-12.2 GHz and 13.5-13.64 GHz.It exhibits reasonably high and stable maximum gains of 5.26 dBi,7.97 dBi and 10.1 dBi and maximum efficiencies of 64%,92%and 98%at the three bands,respectively.Moreover,in the second band,the main beam angle shows a frequency dependence with a total scanning angle of 19°.The miniaturized triple-band antenna has a great potential in wireless communication systems,satellite communication and radar systems.展开更多
A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical pro...A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.展开更多
Objective: To explore the prognostic value of log odds of positive lymph nodes (LODDS) in patients with gastroenteropancreatic neuroendocrine tumors (GEPNET) and to develop nomograms based on LODDS for predicting 1-ye...Objective: To explore the prognostic value of log odds of positive lymph nodes (LODDS) in patients with gastroenteropancreatic neuroendocrine tumors (GEPNET) and to develop nomograms based on LODDS for predicting 1-year, 3-year, and 5-year overall survival (OS) and cancer-specific survival (CSS). Methods: This retrospective cohort study was based on the Surveillance, Epidemiology, and End Results (SEER) Program. Demographic data, clinical data, and survival status were extracted, with endpoints of OS and CSS. Multivariate Cox proportional hazards regression analysis assessed predictors associated with OS and CSS, with hazard ratios (HRs) and 95% confidence intervals (CIs) evaluated. Nomogram performance was assessed by calculating the area under the receiver operating characteristic (ROC) curve (AUC). Results: A total of 1,673 patients were included and divided into a training set (n = 1,172) and a testing set (n = 501). Multivariate Cox proportional hazards regression analyses identified LODDS as an independent prognostic factor for OS (HR = 1.79, 95% CI: 1.44-2.24) and CSS (HR = 1.81, 95% CI: 1.41-2.31). The OS and CSS nomograms, developed from multivariate Cox regression analyses, showed good performance, with AUCs of 0.858, 0.878, and 0.852 for predicting 1-year, 3-year, and 5-year OS, and AUCs of 0.859, 0.887, and 0.865 for 1-year, 3-year, and 5-year CSS in the testing set. The nomograms are accessible online (OS: https://zhmte.shinyapps.io/DynNomapp/;CSS: https:// zhmty.shinyapps.io/DynNomapp/). Conclusions: LODDS serves as an independent prognostic factor in GEPNET. Online nomograms based on LODDS demonstrated effective performance in predicting OS and CSS in GEPNET patients, providing a convenient tool for clinical application.展开更多
We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh ...We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh Log-Logistic (</span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;">) distribution indicate that the distribution can take many shapes depending on the parameter values. The negative skewness and kurtosis indicates that the distribution has li</span><span style="font-family:Verdana;">ghter tails than the normal distribution. The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases. Furthermore, </span></span><span style="font-family:Verdana;">the root mean squared error estimates decay</span><span style="font-family:""><span style="font-family:Verdana;"> towards zero as the sample size increases. This part shows the consistency of the maximum likelihood estimators. From the considered analytical measures, the new </span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;"> provides </span></span><span style="font-family:Verdana;">the best fit to the analysed five real data sets indicating that this new model outclasses its competitors.展开更多
The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of speci...The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.展开更多
The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same...The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.展开更多
Objective: Our aims were to establish novel nomogram models, which directly targeted patients with signet ring cell carcinoma(SRC), for individualized prediction of overall survival(OS) rate and cancer-specific surviv...Objective: Our aims were to establish novel nomogram models, which directly targeted patients with signet ring cell carcinoma(SRC), for individualized prediction of overall survival(OS) rate and cancer-specific survival(CSS).Methods: We selected 1,365 SRC patients diagnosed from 2010 to 2015 from Surveillance, Epidemiology and End Results(SEER) database, and then randomly partitioned them into a training cohort and a validation cohort.Independent predicted indicators, which were identified by using univariate testing and multivariate analyses, were used to construct our prognostic nomogram models. Three methods, Harrell concordance index(C-index), receiver operating characteristics(ROC) curve and calibration curve, were used to assess the ability of discrimination and predictive accuracy. Integrated discrimination improvement(IDI), net reclassification improvement(NRI) and decision curve analysis(DCA) were used to assess clinical utility of our nomogram models.Results: Six independent predicted indicators, age, race, log odds of positive lymph nodes(LODDS), T stage, M stage and tumor size, were associated with OS rate. Nevertheless, only five independent predicted indicators were associated with CSS except race. The developed nomograms based on those independent predicted factors showed reliable discrimination. C-index of our nomogram for OS and CSS was 0.760 and 0.763, which were higher than American Joint Committee on Cancer(AJCC) 8 th edition tumor-node-metastasis(TNM) staging system(0.734 and 0.741, respectively). C-index of validation cohort for OS was 0.757 and for CSS was 0.773. The calibration curves also performed good consistency. IDI, NRI and DCA showed the nomograms for both OS and CSS had a comparable clinical utility than the TNM staging system.Conclusions: The novel nomogram models based on LODDS provided satisfying predictive ability of SRC both in OS and CSS than AJCC 8 th edition TNM staging system alone.展开更多
基金Supported by NSFC (No.12361027)NSF of Inner Mongolia (No.2018MS01021)+1 种基金NSF of Shandong Province (No.ZR2020QA009)Science and Technology Innovation Program for Higher Education Institutions of Shanxi Province (No.2024L533)。
文摘In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.
基金Supported by the National Natural Science Foundation of China,No.82473195 and No.32370797the Natural Science Foundation of Zhejiang Province,No.LTGY23H160018+3 种基金the Zhejiang Medical and Health Science and Technology Program,No.2024KY789 and No.2023KY615the National Research Center for Translational Medicine at Shanghai Program,No.NRCTM(SH)-2025-07the Beijing Science and Technology Innovation Medical Development Foundation,No.KC2023-JX-0270-07the Key Laboratory of Prevention,Diagnosis and Therapy of Upper Gastrointestinal Cancer of Zhejiang Province,No.2022E10021.
文摘BACKGROUND The log odds of positive lymph nodes(LODDS)are correlated with survival outcomes in gastric cancer(GC)patients.However,the prognostic value across different tumor differentiation levels remains unclear.AIM To evaluate the independent prognostic value of LODDS and the stratified predictive efficacy in GC patients with different histologic differentiations.METHODS We conducted a retrospective analysis of 2103 GC patients who underwent radical gastrectomy at Zhejiang Cancer Hospital.The prognostic value of LODDS was compared with that of other lymph node-based metrics,including the pathologic N stage,number of positive lymph nodes,number of total lymph nodes,and lymph node ratio,stratified by tumor differentiation.RESULTS LODDS was identified as an independent prognostic factor for overall survival in moderately to poorly differentiated GC patients.LODDS demonstrated superior predictive accuracy over other lymph node metrics.A nomogram incorporating LODDS,age,carbohydrate antigen(CA)125,carcinoembryonic antigen,and tumor differentiation showed good predictive accuracy(C-index=0.703).A higher LODDS was significantly associated with an increased risk of recurrence or metastasis,poorly differentiated tumors,advanced cancer,mucinous gastric adenocarcinoma,nerve invasion,and vascular tumor thrombus.Additionally,LODDS was positively correlated with the tumor markers CA19-9,CA72-4,CA125,and CA242(all P<0.05).CONCLUSION LODDS is an independent prognostic indicator for patients with moderately and poorly differentiated GC,and its predictive performance is superior to that of other models.
基金supported in part by the Natural Science Foundation of Tianjin(No.19JCYBJC16100)the Tianjin Innovation and Entrepreneurship Training Program(No.202210060027)。
文摘A triple-band miniaturized end-fire antenna based on the odd modes of spoof surface plasmonic polariton(SSPP)waveguide resonator is proposed in this paper.To meet the ever increasing demand for more communication channels and less antenna sizes,multi-band antennas are currently under intensive investigation.By a novel feeding method,three odd modes are excited on an SSPP waveguide resonator,which performs as an end-fire antenna operating at three bands,7.15-7.26 GHz,11.6-12.2 GHz and 13.5-13.64 GHz.It exhibits reasonably high and stable maximum gains of 5.26 dBi,7.97 dBi and 10.1 dBi and maximum efficiencies of 64%,92%and 98%at the three bands,respectively.Moreover,in the second band,the main beam angle shows a frequency dependence with a total scanning angle of 19°.The miniaturized triple-band antenna has a great potential in wireless communication systems,satellite communication and radar systems.
文摘A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.
文摘Objective: To explore the prognostic value of log odds of positive lymph nodes (LODDS) in patients with gastroenteropancreatic neuroendocrine tumors (GEPNET) and to develop nomograms based on LODDS for predicting 1-year, 3-year, and 5-year overall survival (OS) and cancer-specific survival (CSS). Methods: This retrospective cohort study was based on the Surveillance, Epidemiology, and End Results (SEER) Program. Demographic data, clinical data, and survival status were extracted, with endpoints of OS and CSS. Multivariate Cox proportional hazards regression analysis assessed predictors associated with OS and CSS, with hazard ratios (HRs) and 95% confidence intervals (CIs) evaluated. Nomogram performance was assessed by calculating the area under the receiver operating characteristic (ROC) curve (AUC). Results: A total of 1,673 patients were included and divided into a training set (n = 1,172) and a testing set (n = 501). Multivariate Cox proportional hazards regression analyses identified LODDS as an independent prognostic factor for OS (HR = 1.79, 95% CI: 1.44-2.24) and CSS (HR = 1.81, 95% CI: 1.41-2.31). The OS and CSS nomograms, developed from multivariate Cox regression analyses, showed good performance, with AUCs of 0.858, 0.878, and 0.852 for predicting 1-year, 3-year, and 5-year OS, and AUCs of 0.859, 0.887, and 0.865 for 1-year, 3-year, and 5-year CSS in the testing set. The nomograms are accessible online (OS: https://zhmte.shinyapps.io/DynNomapp/;CSS: https:// zhmty.shinyapps.io/DynNomapp/). Conclusions: LODDS serves as an independent prognostic factor in GEPNET. Online nomograms based on LODDS demonstrated effective performance in predicting OS and CSS in GEPNET patients, providing a convenient tool for clinical application.
文摘We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh Log-Logistic (</span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;">) distribution indicate that the distribution can take many shapes depending on the parameter values. The negative skewness and kurtosis indicates that the distribution has li</span><span style="font-family:Verdana;">ghter tails than the normal distribution. The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases. Furthermore, </span></span><span style="font-family:Verdana;">the root mean squared error estimates decay</span><span style="font-family:""><span style="font-family:Verdana;"> towards zero as the sample size increases. This part shows the consistency of the maximum likelihood estimators. From the considered analytical measures, the new </span><i><span style="font-family:Verdana;">KORLL</span></i><span style="font-family:Verdana;"> provides </span></span><span style="font-family:Verdana;">the best fit to the analysed five real data sets indicating that this new model outclasses its competitors.
基金Sponsored by the Scientific Research Fund of Heilongjiang Provincial Education Department (11541109)the Science Foundation of Harbin Normal University (KM2007-11)
文摘The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.
文摘The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.
文摘Objective: Our aims were to establish novel nomogram models, which directly targeted patients with signet ring cell carcinoma(SRC), for individualized prediction of overall survival(OS) rate and cancer-specific survival(CSS).Methods: We selected 1,365 SRC patients diagnosed from 2010 to 2015 from Surveillance, Epidemiology and End Results(SEER) database, and then randomly partitioned them into a training cohort and a validation cohort.Independent predicted indicators, which were identified by using univariate testing and multivariate analyses, were used to construct our prognostic nomogram models. Three methods, Harrell concordance index(C-index), receiver operating characteristics(ROC) curve and calibration curve, were used to assess the ability of discrimination and predictive accuracy. Integrated discrimination improvement(IDI), net reclassification improvement(NRI) and decision curve analysis(DCA) were used to assess clinical utility of our nomogram models.Results: Six independent predicted indicators, age, race, log odds of positive lymph nodes(LODDS), T stage, M stage and tumor size, were associated with OS rate. Nevertheless, only five independent predicted indicators were associated with CSS except race. The developed nomograms based on those independent predicted factors showed reliable discrimination. C-index of our nomogram for OS and CSS was 0.760 and 0.763, which were higher than American Joint Committee on Cancer(AJCC) 8 th edition tumor-node-metastasis(TNM) staging system(0.734 and 0.741, respectively). C-index of validation cohort for OS was 0.757 and for CSS was 0.773. The calibration curves also performed good consistency. IDI, NRI and DCA showed the nomograms for both OS and CSS had a comparable clinical utility than the TNM staging system.Conclusions: The novel nomogram models based on LODDS provided satisfying predictive ability of SRC both in OS and CSS than AJCC 8 th edition TNM staging system alone.
