Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.

Subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization

Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.

MODELING OF 3-D IMAGES AND SPACE MARKOV CUBIC MESH MODELS

Three-dimensional(3-D)Markov cubic random mesh models are presented andproved in the form of two theorems in details.Its applications to the modeling and description of3-D images are described.The model presented here is a appropriate mathematical tool for thesegmentation,modeling,classification and other processing.Finally,an example is given.

Enhancing asphaltene precipitation modeling by cubic-PR solid model using thermodynamic correlations and averaging techniques

Cubic equation-of-state solid models are one of the most widely used models to predict asphaltene precipitation behavior.Thermodynamic parameters are needed to model precipitation under different pressures and temperatures and are usually obtained through tuning with multi asphaltene onset experiments.For the purpose of enhancing the cubic Peng–Robinson solid model and reducing its dependency on asphaltene experiments,this paper tests the use of aromatics and waxes correlations to obtain these thermodynamic parameters.In addition,weighted averages between both correlations are introduced.The averaging is based on reported saturates,aromatics,resins,asphaltene(SARA)fractions,and wax content.All the methods are tested on four oil samples,with previously published data,covering precipitation and onset experiments.The proposed wax-asphaltene average showed the best match with experimental data,followed by a SARA-weighted average.This new addition enhances the model predictability and agrees with the general molecular structure of asphaltene molecules.

CYCLIC DEFORMATION OF FACE CENTERED CUBIC CRYSTALS AND ITS DISLOCATION INTERACTION MODEL——Ⅱ.DISLOCATION INTERACTION MODEL OF CYCLIC DEFORMATION

A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac- cording to this model,cyclic stress-strain responses and saturation dislocation structures of a crystal are associated with the modes and intensities of dislocation interactions between slip systems active in the crystal; and,hence,may be predicted by the location of its tensile axis in the crystallographic triangle.This model has successfully explained the different behaviours of double-slip crystals and multi-slip behaviours of some crystals with orientations usually con- sidered as single-slip ones.

A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

某院药品消耗指数与DRG超支的相关性及阈值效应分析

目的探讨药品消耗指数与疾病诊断相关分组(DRG)超支的相关性,为医院优化费用结构、加强精细化管理提供依据。方法以某三级甲等医院2023年9-11月DRG入组病例为研究资料,分别采用Logistic回归模型、限制性立方样条(RCS)模型分析药品消耗指数与DRG超支的相关性以及阈值效应。同时基于药品消耗指数开展合理用药点评,进行精准控费及管理,并分析管控前(2023年1-6月)与管控后(2024年1-6月)全院主要药事指标变化情况。结果多因素Logistic回归分析结果显示,住院天数长、药品消耗指数高、转科、合并糖尿病是DRG超支的危险因素(P<0.05)。RCS模型结果表明,药品消耗指数与DRG超支呈非线性关系,当药品消耗指数≥0.64时,药品消耗指数与DRG超支风险呈正相关(P<0.05)。与管控前同期比较,管控后的次均医疗费用、次均药品费用、药品消耗指数均显著下降(P<0.01)。结论药品消耗指数是DRG超支的危险因素,其与DRG超支存在非线性关系和阈值效应。各医院可结合实际药品使用情况、疾病谱特征以及成本控制目标,综合考虑医疗质量、患者需求和医保支付能力等因素,设定合理的阈值并实施动态监测与干预,以实现药品使用的精准管控。

Constructing B-rep Solid Model from Cubic Volume Cells

The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B-rep solid model and conStrUcts the B-rep geometric clementS with an approach frombottom to up. Once the B-rep model is established, it is efficient in displaying because inner voxels areomitted and many coplanar facetS are merged together. By displaying the interSeCtion lines of theconstructed B-reP model and the partitioning planes, the tessellation image can be generated.

中小学生高度近视发生风险预测模型:基于巢式病例对照研究

背景中小学生由于学习压力、电子产品普及以及不良用眼习惯,视力健康问题日益严重,成为近视的高发群体,高度近视作为近视的严重阶段,已成为全球范围内的公共卫生问题。尽管现有诸多研究对近视的危险因素进行了探讨,但鲜有研究针对性阐明风险因素与高度近视发生的复杂非线性关系,本研究结合巢式病例对照研究和限制性立方样条,开发一个中小学生高度近视风险预测模型,通过早期识别高风险个体,延缓或阻止高度近视的发展,实现近视的三级预防,对中小学生的学业和生活质量有积极意义。目的探究中小学生高度近视的流行现状及危险因素,构建风险预测模型,为中小学生高度近视防控提供科学依据。方法采用巢式病例对照研究,于2023年选取杭州市12所学校中度近视的学生作为研究对象建立队列,按照全国学生常见病和健康影响因素监测与干预工作方案,对纳入研究的中小学生开展近视状况监测,研究期间进展为高度近视的中小学生作为高度近视发生组,其余未进展为高度近视的中小学生作为对照组,对两组研究对象开展视力保健行为进行调查。采用Lasso回归筛选特征变量后进行多因素Logistic回归分析探究中小学生高度近视发生的影响因素,并采用列线图对风险预测模型可视化,同时采用Hosmer-Lemeshow检验、受试者工作特征(ROC)曲线、Calibration曲线、决策曲线分析(DCA)对模型性能进行评估,最后采用限制性立方样条进一步明确年龄与高度近视发生风险的关系。结果12所中小学校共纳入2468名学生,未进展为高度近视的学生1293名,中度近视进展为高度近视的学生1175名,高度近视发生率为47.61%(1175/2468)。两组学生年龄、年级、BMI、每日入睡时间、地区、户外活动时间、电子产品使用时间、课后作业时间、家用台灯比较,差异有统计学意义(P<0.05)。Lasso回归筛选出8个特征变量:年级、BMI、每日入睡时间、地区、户外活动时间、电子产品使用时间、课后作业时间、家用台灯。多因素Logistic回归分析结果显示,初中年级(OR=2.612,95%CI=2.185~3.127),超重或肥胖(OR=2.140,95%CI=1.458~3.169)、偏瘦(OR=1.807,95%CI=1.430~2.290),每日入睡时间在22:00之后(OR=1.408,95%CI=1.188~1.670),户外活动时间1~2 h/d(OR=1.371,95%CI=1.122~1.675)、<1 h/d(OR=1.648,95%CI=1.342~2.027),电子产品使用时间>2 h/d(OR=1.440,95%CI=1.119~1.856),课后作业时间1~2 h/d(OR=1.461,95%CI=1.126~1.899)、>2 h/d(OR=1.534,95%CI=1.218~1.935)为中小学生高度近视发生的危险因素(P<0.05);而高中年级(OR=0.560,95%CI=0.419~0.743)为中小学生高度近视发生的保护因素(P<0.05)。基于年级、BMI、每日入睡时间、户外活动时间、电子产品使用时间、课后作业时间等6个变量构建的预测模型ROC曲线下面积为0.840(95%CI=0.825~0.855),具有良好的拟合优度、一致性、应用性,限制性立方样条分析显示13~15岁为高度近视的高发年龄段。结论中小学生高度近视发生率较高,风险预测模型为高度近视的预防和控制提供了科学依据,应在初中年级加强近视防控措施,改善学生的视力保健行为,降低高度近视的发生。

使用鱼眼镜头制作QuickTime CubicVR

讨论了最新的QuickTime CubicVR技术的几种合成方法,并就其中最简单易行的鱼眼镜头法进行了深入的探讨,得到了这种方法的数学模型,为以后的软件开发奠定了基础。

红细胞分布宽度/白蛋白比值与老年脓毒症患者1年内死亡风险的关系

目的探讨红细胞分布宽度/白蛋白比值(red cell distribution width/albumin ratio,RAR)与老年脓毒症患者1年内死亡风险的关系。方法本研究为回顾性研究,数据来自美国重症监护医学信息数据库Ⅳ(MIMICⅣ2.2)。主要结局是老年脓毒症患者1年内出现的死亡事件。首先采用Boruta算法确定RAR的重要性。进而,构建多因素Cox回归模型,并以限制立方样条回归曲线评估RAR与老年脓毒症患者1年内死亡事件的关联。采用Kaplan-Meier生存分析,对出现终点事件差异进行估计。最后用亚组分析来评估结果的稳健性。结果共纳入3018例年龄≥65岁的脓毒症患者,1年内病死率为60.8%。多因素Cox回归分析显示,RAR与老年脓毒症患者1年内死亡风险相关(HR=1.206,P<0.0001)。进一步运用Kaplan-Meier生存曲线进行分析,结果显示,高RAR水平组较低RAR水平组的患者在1年内的病死率显著增高。借助限制立方样条回归模型,显示老年脓毒症患者1年内死亡风险随RAR升高而呈现线性增长。亚组分析表明,急性呼吸衰竭和RAR与1年内死亡事件风险之间存在交互作用(P=0.0477)。Boruta算法表明,RAR是老年脓毒症患者不良结局的重要特征。结论高水平的RAR与老年脓毒症患者1年内死亡风险显著相关,RAR对老年脓毒症患者1年内死亡风险具有良好的预测价值。

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

New insight into prediction of phase behavior of natural gas hydrate by different cubic equations of state coupled with various mixing rules

Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.

基于3种非线性回归模型的薄壳山核桃果实生长发育研究

以波尼、马汉、卡多、赛普洛斯、贝壳等薄壳山核桃品种为试验对象,定期对核桃果实的纵径、横径的生长量进行观测,通过果实解剖掌握果实的发育阶段,最后分别应用Logistic模型、二次多项式、三次多项式对果实的两径数据进行拟合。结果表明:各品种果实的两径生长均呈现出典型的“S”形曲线,且纵径的累计生长量始终大于横径;三次多项式对果实的两径拟合效果均优于Logistic模型和二次多项式,其中三次多项式的拟合系数均超过0.991,且与实测数据的相关性均达到极显著水平,表明三次多项式能够更好地拟合薄壳山核桃果实的发育过程。拟合方程可确定不同品种果实发育的各个时间节点,结合果实解剖结果,可揭示各品种果实的发育进程。

Exact parametric representations of orbits defined by cubic Hamiltonian

In this paper,we show that for any given planar cubic algebraic curves defined by a quadratic Hamiltonian vector field,we can always have their exact explicit parametric representations. We use a model of micro-structured solid to show an application of our conclusions.

高校安全教育立方体模型构建与数字化建设思路

高校安全是国家安全体系的重要组成部分,也是确保学生健康成长、全面发展的重要基石,对于营造和谐校园环境、构筑平安中国具有重要意义。随着教育数字化转型的深入推进,如何通过信息化、数字化建设,系统优化和丰富安全教育的内容与形式,提升教育培训的质量与效率,成为高校安全管理人员亟需重视的问题。为此,文章针对国内外高校安全教育实践进行了系统的梳理与分析,首先从“教育主题”“课程形式”“面向群体”三维度构建了高校安全教育立方体模型,然后阐述了基于模型的安全教育体系的主要内容,最后提出高校安全教育数字化系统的建设思路,旨在为高校安全教育的数字化转型提供理论支持和实践指导,以助力高校安全教育能力的提升。

孕期血清铁蛋白动态变化及其与分娩结局的相关性

目的分析孕期血清铁蛋白(SF)水平的动态变化,探讨不同孕周SF水平与分娩结局的相关关系。方法选取2021年1月至2023年8月期间,在安徽医科大学第一附属医院东城院区规律产检且连续3次SF检测的孕妇665名作为研究对象。分析孕期SF的动态变化,用线性回归模型和限制性立方样条分析不同孕周SF与分娩结局间的相关性,并构建SF动态变化与分娩结局的群组轨迹模型。结果随着孕周增加,SF水平下降,铁缺乏率增加。线性相关性分析显示孕8~16周、孕16~24周SF与分娩结局相关性无统计学意义(P>0.05);孕24-32周SF水平与新生儿身长(β:−0.009,95%CI:−0.015~−0.003)、新生儿体质量(β:−3.331,95%CI:−5.201~−1.461)及分娩孕周(β:−0.013,95%CI:−0.019~−0.008)呈负相关。限制性立方样条曲线拟合显示,孕8~16周SF、孕16~24周SF与分娩结局相关性无统计学意义(P整体>0.05),孕24~32周SF与分娩孕周和新生儿身长呈线性剂量-反应关系(P整体<0.05,P非线性>0.05),与新生儿体质量呈非线性相关关系(P整体<0.05,P非线性<0.05)。群组轨迹模型显示,SF浓度下降较快组早产率高于SF浓度下降中等组和较慢组(P<0.01),SF不同变化轨迹类型与新生儿体重相关性无统计学意义。结论孕24~32周SF水平升高与分娩孕周、新生儿身长和体质量相关,孕期SF持续下降与早产发生风险增加有关。

Investigation of cost-effectiveness of highway asphalt pavement maintenance treatments based on rutting development analysis

To investigate the cost-effectiveness of different maintenance treatments of highways in Jiangsu Province, the historical pavement maintenance records, traffic load information and pavement performance data in the pavement management system （PMS） are recorded and analyzed. Compared with the growth model, the linear model, the logarithm model and the exponential model, the cubic model has higher regression accuracy R2 and it can capture the sigmoid shape of the deterioration curve. So it is selected to simulate the pavement rotting development. The benefit over cost ratio is calculated to quantify the treatment cost- effectiveness. The analysis results show that thin hot mix asphalt （HMA） overlays and micro surfacing are more cost- effective than the. other two treatments on light and moderate traffic roads. Hot in-place recycling and thick HMA overlays have much longer service lives and greater cost-effectiveness under heavy or extra heavy traffic.