This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli an...This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.展开更多
基金supported by the Science and Technology Development Fund of Macao SAR(FDCT0128/2022/A,0020/2023/RIB1,0111/2023/AFJ,005/2022/ALC)the Shandong Natural Science Foundation of China(ZR2020MA004)+2 种基金the National Natural Science Foundation of China(12071272)the MYRG 2018-00168-FSTZhejiang Provincial Natural Science Foundation of China(LQ23A010014).
文摘This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fundamental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.
文摘目的:探讨降钙素原(procalcitonin,PCT)和可溶性白细胞分化抗原14亚型(soluble cell differentiation antigen 14,sCD14,又称presepsin,PSPN)对急性髓系白血病(acute myeloid leukemia,AML)化疗期间发热性中性粒细胞减少症(febrile neutropenia,FN)患者细菌感染的鉴别价值。方法:纳入2018年07月至2022年02月期间在我院接受化疗且出现FN的121例AML患者,分为非细菌感染组化疗期间发生FN且发热原因不明(细菌培养阴性,无临床迹象表明存在感染)与细菌感染组菌血症(血培养阳性)和局部感染(血培养阴性,细菌培养提示局部感染)。通过酶联免疫吸附试验试剂盒检测FN发病第1至3天血浆PCT和PSPN水平。结果:与非细菌感染组相比,细菌感染组患者FN发病第1至3天的PCT和PSPN水平明显更高,差异有统计学意义(P<0.05)。第1、2、3天的PCT水平鉴别FN细菌感染的曲线下面积(area under the curve,AUC)分别为0.882、0.737、0.715,而PSPN诊断AUC分别为0.799、0.729、0.703。此外,PCT和PSPN联用可进一步提高对FN细菌感染诊断的AUC值(0.892、0.808、0.763)。发病第1天PCT≥2.02 ng/mL或者PSPN≥2.40μg/L,FN细菌感染风险显著增加(P<0.05);校正混杂因素后,当PSPN≥2.91μg/L时,AML患者FN细菌感染风险增加2.177~2.624倍(P<0.05)。Spearman相关性分析显示PCT与细菌性脓毒症患者序贯器官功能衰竭评分(sequential organ failure assessment,SOFA)呈正相关(P<0.001),PSPN值与SOFA评分无显著相关性(P>0.05)。结论:PCT较PSPN在区分FN细菌感染性病因和非感染病因方面准确性更高,其浓度与细菌性脓毒症的严重程度有关;二者联用能进一步提高PCT对FN细菌感染的诊断效能。
