Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nat...Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are展开更多
In this paper,we consider the generalized Nash equilibrium with shared constraints in the stochastic environment,and we call it the stochastic generalized Nash equilibrium.The stochastic variational inequalities are e...In this paper,we consider the generalized Nash equilibrium with shared constraints in the stochastic environment,and we call it the stochastic generalized Nash equilibrium.The stochastic variational inequalities are employed to solve this kind of problems,and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed.We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations.The properties of the stochastic quadratic generalized Nash equilibrium are shown.The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed.Moreover,we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions,and we also analyze the properties of the formulations.Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties,such as robustness,low risk and so on.展开更多
基金supported by the research grants Seed ProjectPrince Sultan UniversitySaudi Arabia SEED-2022-CHS-100.
文摘Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are
基金National Natural Science Foundation of China(No.11601541,No.12171027)State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of SciencesYouth Foundation of Minzu University of China(No.2021QNPY98).
文摘In this paper,we consider the generalized Nash equilibrium with shared constraints in the stochastic environment,and we call it the stochastic generalized Nash equilibrium.The stochastic variational inequalities are employed to solve this kind of problems,and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed.We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations.The properties of the stochastic quadratic generalized Nash equilibrium are shown.The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed.Moreover,we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions,and we also analyze the properties of the formulations.Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties,such as robustness,low risk and so on.
文摘目的探索运用标准差指数（standard deviation index，SDl）和变异系数指数（coefficient of variation radio, CVR）对比分析同一实验室内不同血细胞分析仪检NWBC、RBC、血红蛋白（hemoglobin，Hb）、血细胞比容（hematocrit，HCT）和血小板（platelets，PLT）计数项目的室内质量控制比对检测结果的一致性，及其评价方法的新模式。方法分析2014年5月1日至5月31日期间，宁夏医科大学总医院医学实验中心不同型号的5台血细胞分析仪检测WBC（流式细胞计数法）、RBC（鞘流DC检测法）、Hb（十二烷基硫酸钠血红蛋白检测法）、HCT（脉冲高度检测法）和PLT（鞘流DC检测法）5N血常规项目三个水平的室内质量控制数据，计算出75组均值㈤、标准差（standard deviation，SD）、及变异系数（coefficient of varation，CV），以及各项目的SDI、CVR等；同时评价分析不同血细胞分析仪检测各项目的日间精密度分布及比对分析检测结果正确度的一致性。结果根据5台血细胞分析仪2014年5月，连续31d中，检测wBC、RBC、Hb、HCT、PLT项目1～3的三个水平共465个质控数据。5个项目各水平的SDIYfICVR分别为-1．37～1．84和0．72～1．46、-3．35～2．59和0．83～1．21、～3．28～3．S7和0．40～1．67、-2．79～1．88和0．53～1．61、-1．25～1．21和0．52～1．59。其中，RBC和HGB3个水平室内质控结果SDI〉2的数量最多，分别为5个和7个；HCT有1＋SDI〉2；WBC和PLT的SDI〈2。WBC、RBC、Hb、HCT、PLT的SDI指标不合格率分别为0、33．33％、46．67％、6．67％、0。每台仪器检测5个项目CVR与所有实验室仪器CVR相比均〈2。结论运用SDI和CVR综合评价实验室内不同血细胞分析仪检测同一WBC、RBC、Hb、HCT、PLT项目结果的正确度和精密度的室内质量控制的可比性较好，可作为实验室内不同血细胞分析仪检测相同项目结果一致性评价的实验室内质量控制新模
