A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.

不同储藏温度下鲜猪肉微生物菌群及TVB-N的Logistic生长曲线模型分析

为研究鲜猪肉在不同储藏温度下主要腐败菌及其总挥发性盐基氮(TVB-N)含量随时间的变化规律,找出其变化函数模型。选取(-3±0.5)、(0±0.5)、(4±0.5)、(10±0.5)℃四个储藏温度组,每组设置0、10、20、34、48、72、96 h 7个不同的储藏时间,测定鲜猪肉细菌菌落总数、大肠杆菌等6个微生物指标和TVB-N含量,对各指标的时间序列值在4个储藏温度组间进行配对T检验,并建立Logistic生长曲线函数模型。结果表明:不同储藏温度组鲜猪肉各指标间存在极显著差异;各指标在不同储藏温度下与自变量时间t的Logistic生长曲线函数的决定系数R2均大于0.9;以总挥发性盐基氮含量为指标,得出理论上(0±0.5)℃储藏不超过76 h的为鲜猪肉,超过76 h不超过121 h的为次鲜肉。综合分析,鲜猪肉建议(0±0.5)℃储藏为宜,储藏时间不超过121 h。研究结果可为鲜猪肉储藏保鲜提供参考。

学习者在线动态学习成绩的Logistic曲线增长规律及其聚类研究

基于信息化教学中的动态学习数据,采用Logistic曲线拟合学习者的综合在线学习成绩随学习时长的增长规律,可将无穷维函数空间转化为有限维的参数空间,并借助于经典的K-Means聚类算法实现学习者的综合在线学习成绩增长规律的聚类。研究结果表明:学习者可被分为主流学习者和非主流学习者两大类别;主流学习者占全部学习者的96.92%,且可被进一步细分为高效学习者、中效学习者、低效学习者,占全部学习者的比例分别为16.41%、61.02%和19.49%;非主流学习者可被分为长期缓增型学习者和短期陡增型学习者,占全部学习者的比例均为1.54%。此外,不同类别学习者之间的期末考试平均成绩存在显著差异,主流学习者中高效学习者、中效学习者和低效学习者的期末考试平均成绩逐渐递减,但均高于非主流学习者的期末考试平均成绩;在非主流学习者中,短期陡增型学习者的期末考试平均成绩高于长期缓增型学习者的期末考试平均成绩。

时滞扩散型Logistic方程解的稳定性

研究了一类时滞扩散型Logistic方程带有Neumann边界条件的初边值问题解的稳定性.利用能量估计的方法,借助于Halanay不等式,证明了当方程系数满足一定条件时,解以指数收敛到常数值的稳态解.

电导法结合Logistic方程评价6个文冠果种质抗寒性

为了评价引进的文冠果种质的抗寒性,为其进一步栽培和育种利用提供参考,以引进的6份文冠果种质(G27、BD12、BD特异、建2、株系2和G13)为试材,设置-10、-20、-30℃3个低温胁迫处理,测定相对电导率,并拟合Logistic方程计算半致死温度(LT_(50))。结果表明,供试种质BD特异、G27、BD12、建2、G13、株系2的半致死温度分别为-13.272、-12.244、-11.543、-8.246、-5.643、-2.642℃,依据半致死温度评价抗寒性强弱为BD特异>G27>BD12>建2>G13>株系2。电导法结合Logistic方程评价文冠果种质抗寒性的结果与前期研究结果基本一致,该方法可作为评价种质抗寒性的简要方法之一,该研究结果可为引进种质进一步在新疆地区栽培与育种利用提供参考。

Furnace Temperature Curve Optimization Model Based on Differential Evolution Algorithm

When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on optimizing the furnace temperature curve under varying settings of reflow oven zone temperatures and conveyor belt speeds.To address this,the research sequentially develops a heat transfer model for reflow soldering,an optimization model for reflow furnace conditions using the differential evolution algorithm,and an evaluation and decision model combining the differential evolution algorithm with the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method.This approach aims to determine the optimal furnace temperature curve,zone temperatures of the reflow oven,and the conveyor belt speed.

利用Logistic曲线预测二氧化碳累计封存量和注入速度增长率——以英国地区为例

英国提出了净零目标,计划到2050年二氧化碳排放量降为零,实现75~175Mt/a的二氧化碳注入速度。以英国为研究对象,利用逻辑模型预测其二氧化碳累计封存量和注入速度增长率。由于没有历史注入数据来进行逻辑增长曲线的拟合,所以采用地质封存量和目标注入速度作为模型的约束条件。英国地区很早就进行了二氧化碳地质封存潜力评价,所有相关地质数据均可在二氧化碳封存数据库(CO_(2)Stored)中获取。模拟结果表明,从2026年起,注入速度以每年3.8%的速度增长,可满足净零目标75Mt/a的最低注入速度要求,2050年累计封存量2.62Gt。如果在2035年将注入速度年增长率由3.8%提高至4.6%,虽然可以封存更多的二氧化碳,但无法在2050年达到175Mt/a的注入速度目标。如果英国的二氧化碳捕获和储存项目晚于2026年开始,则需要更高的注入速度增长率来满足净零目标。

基于Logistic回归模型及ROC曲线的糖尿病足溃疡复发的危险因素分析

目的基于Logistic回归模型及ROC曲线的糖尿病足溃疡(DFU)复发的危险因素分析。方法回顾性选取2018年9月—2019年9月本院收治的92例初发2型糖尿病(T2DM)足溃疡患者,根据3年内足溃疡复发情况分为非复发组51例与复发组41例,行DFU患者足溃疡复发的单因素分析,多因素Logistic模型研究DFU患者足溃疡复发的危险因素,Spearman检验分析各指标与DFU患者足溃疡复发的相关性,受试者工作特征曲线(ROC)评价模型诊断效能。结果92例DFU患者随访3年,复发41例,复发率为44.57%。单因素分析显示,两组体质量指数(BMI)、性别、心脑血管疾病病史占比、高血压病史占比、住院时间、发病至就诊时间、ALB、TBIL、Scr、HbA1c、TG、HDL、TC、LDL差异无统计学意义(P>0.05);与非复发组比较,复发组年龄、T2DM病程、糖尿病周围神经病变(DPN)占比、下肢外周动脉病变(PAD)占比、吸烟史占比、创面位于胼胝占比明显升高,TBIL水平明显降低(均P<0.05)。多因素分析显示,年龄增大、T2DM病程长、合并DPN、合并PAD、有吸烟史、创面位于胼胝及血清TBIL水平降低为DFU患者足溃疡复发的危险因素(P<0.05)。Spearman检验提示,DFU患者足溃疡复发与年龄、T2DM病程、DPN、PAD、吸烟史、创面位于胼胝呈正相关,TBIL水平明显降低呈负相关(均P<0.05)。以unite(七变量综合)、年龄、T2DM病程、TBIL、DPN、PAD、吸烟、创面位于胼胝为检验变量绘制ROC曲线,结果显示,unite的AUC值为0.834,分别大于年龄(0.632)、T2DM病程(0.619)、TBIL(0.645)、DPN(0.684)、PAD(0.662)、吸烟(0.640)、创面位于胼胝(0.677),提示7项指标联合应用于评估DFU患者足溃疡复发的效能明显优于单一指标(P<0.05)。结论年龄增大、T2DM病程长、合并DPN、合并PAD、有吸烟史、创面位于胼胝、血清TBIL水平降低为DFU患者足溃疡复发的危险因素,如发现上述情况应高度警惕DFU患者足溃疡复发风险,并尽早干预。

Deformable分数阶Logistic微分方程的解

该文基于Deformable分数阶微积分定义框架,讨论一类分数阶Logistic微分方程初值问题,得到了解析解,并给出相应的数值模拟结果.

CALCULATIONS OF THE PHASE EQUILIBRIA AND CRITICAL CURVES WITH THE EQUATION OF STATE FOR BINARY MIXTURES

A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.

决策树C5.0与Logistic回归模型对产后腹直肌分离预测性能的比较研究

目的比较决策树C5.0与Logistic回归模型对产后腹直肌分离的预测效果。方法选取产后复查的产妇476例作为研究对象。采用问卷调查法获取产妇的一般资料;采用电刺激治疗仪评估盆底肌电值;采用腹部触诊法判断腹直肌分离程度。将所有数据按照3∶2的比例建立训练集与测试集,运用决策树C5.0及Logistic回归建立产后腹直肌分离的风险预测模型;采用准确度、灵敏度、特异度、约登指数、阴性预测值、阳性预测值和受试者工作特征(ROC)曲线的曲线下面积(AUC)对模型的预测性能进行比较。结果在训练集中,决策树C5.0和Logistic回归模型的准确度分别为96.94%、72.45%,灵敏度分别为98.92%、86.02%,特异度分别为93.52%、49.07%,阳性预测值分别为96.34%、74.42%,阴性预测值分别为98.06%、67.09%,约登指数分别为92.44%、35.10%,AUC分别为0.962、0.675;训练集中,决策树C5.0和Logistic回归模型的AUC比较,差异有统计学意义(P<0.05)。在测试集中,决策树C5.0与Logistic回归模型的准确率分别为81.50%、62.43%,灵敏度分别为88.35%、82.52%,特异度分别为71.43%、32.86%,阳性预测值分别为81.98%、64.39%,阴性预测值分别为80.65%、56.10%,约登指数分别为59.78%、15.38%,AUC分别为0.799、0.577;测试集中,决策树C5.0和Logistic回归模型的AUC比较,差异有统计学意义(P<0.05)。结论决策树C5.0对产后腹直肌分离的预测效能优于Logistic回归模型。

逻辑斯谛(logistic)人口模型的起源与早期发展

通过对几篇原始文献的解读,介绍逻辑斯谛(logistic)人口模型的起源和早期发展.从中可以体会到,数学知识往往并不像大多数教科书叙述的那样简单、直线式发展,而是由众多学者接力式地甚至断断续续地呈现到我们眼前.教师和教材在传授这些知识的同时,如果也能讲述一点起源与发展史,对学生数学能力和数学素质的培养是有益的.

ANALYTIC INVARIANT CURVES OF A NONLINEAR SECOND ORDER DIFFERENCE EQUATION

This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S^1 and the case on S^1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.

Improved Nonlinear Equation Method for Numerical Prediction of Jominy End-Quench Curves

Without considering the effects of alloying interaction on the Jominy end-quench curves, the prediction resuits obtained by YU Bai-hai＇s nonlinear equation method for multi-alloying steels were different from those experimental ones reported in literature. Some alloying elements have marked influence on Jominy end-quench curves of steels. An improved mathematical model for simulating the Jominy end-quench curves is proposed by introducing a parameter named alloying interactions equivalent （Le）. With the improved model, the Jominy end-quench curves of steels so obtained agree very well with the experimental ones.

基于Logistic回归的住院精神障碍患者医院感染危险因素预测

目的 运用Logistic回归模型和受试者工作特征(ROC)曲线探讨住院精神障碍患者发生医院感染危险因素并分析预测价值,为精神卫生专科医疗机构临床实践和感染控制及预防提供参考依据。方法 回顾性调查收集2022年1月~12月间某三级甲等精神卫生专科医院9 989例住院患者病历资料,采用Logistic回归分析医院感染危险因素并进行预测,应用ROC曲线进行预测价值评价。结果 9 989例患者中发生医院感染201例,感染发病率2.01%,医院感染203例次,感染例次发病率2.03%,感染部位分布主要以上、下呼吸道为主,共175例次,构成比占86.21%。单因素分析结果显示,性别、年龄、住院天数、精神障碍类型、住院季节、精神类药物、患者管理模式和保护性约束8个因素与住院精神障碍患者医院感染的发生相关,组间相关数据比较差异有统计学意义(P<0.05或0.01)。多因素非条件Logistic回归分析结果显示,患者封闭管理模式、精神类药物≥2种、住院天数>30 d、男性、年龄≥60岁和重型精神障碍患者共6个因素是住院精神障碍患者医院感染的主要独立危险因素,联合预测因子的AUC值为0.735,95%CI为0.701~0.769,其预测价值均优于各单一变量的预测价值。结论 住院精神障碍患者易发生医院感染,应重点关注患者封闭管理模式、精神类药物≥2种、住院天数>30 d、男性、年龄≥60岁和重型精神障碍患者,开展定向目标监测,有针对性地制定相关防控措施,以减少住院精神障碍患者医院感染的发生。

An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations

In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations using Newton iteration method. We give numerical results to satisfy the accuracy and the applicability of the proposed schemes.

GLOBAL ATTRACTIVITY FOR NONAUTONOMOUS DELAY-LOGISTIC EQUATIONS^+

In this paper, sufficient conditions are obtained for the tive steady state of the delay-logistic equation to be a global attractor.An application of the results also solves aa conjecture of Gopalsamy.

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER CURVES

The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.

Modified non-rectangular hyperbola equation with plant height for photosynthetic light-response curves of Potentilla anserina and Elymus nutans at various growth phases in the Heihe River Basin, Northwest China

The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.

Joule-Thomson inversion curve prediction by using equation of state

In this paper five equations of state are tested for checking their ability to predict the Joule-Thomson inversion curve.These five equations of state are:Mohsennia-Modarres-Mansoori(MMM),Ji-Lemp(JL),modified Soave-Redlich-Kwang(SRK)equation of state by Graboski(MSRK1),modified SRK equation of state by Peneloux and Rauzy(MSRK2),and modified Peng-Robinson (PR)equation of state by Rauzy(PRmr).The investigated equations of state give good prediction of the low-temperature branch of the inversion curve,except for MMM equation of state.The high-temperature branch and the peak of the inversion curve have been observed,in general,to be sensitive to the applied equation of state.The values of the maximum inversion temperature and maximum inversion pressure are calculated for each component used in this work.