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双语推荐：C曲线

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给出了一类双参数的类四次三角Bézier曲线及其扩展曲线的定义,得到了该类曲线及其扩展曲线的性质,给出了两段双参数的类四次三角Bézier曲线G1（C1）,G2（C2）及两段扩展曲线G1（C1）,G2（C2）光滑拼接的充要条件,并讨论了这两类曲线的应用。算例表明,该类曲线及其扩展曲线在曲线造型,特别是在非对称图形的造型中,具有很强的描述能力。
A class of quasi-quartic trigonometric polynomial Bézier curves with double parameters and its extension are defined. The properties of the class of the curves and its extension are obtained, and the necessary and sufficient conditions for G1(C1)、G2(C2) continuously joining with two segments of quasi-quartic trigonometric polynomial Bézier curves and two extensions are given. The applications of them are discussed. Experimental examples show that the class of the curves and its extensions have stronger abilities in curve designing, especially in designing of non-symmetry figures.

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在分析四次C-Bézier曲线性质的基础上,通过修改形状参数α和调整控制顶点,分别提出了两种修改四次C-Bézier曲线形状的新方法。分析了控制参数α对曲线形状的影响,并通过调节形状参数实现了四次C-Bézier曲线形状的修改;基于控制顶点与曲线形状关系的几何模型,给出了另一种通过调整控制顶点来修改四次C-Bézier曲线形状的方法,实现了曲线整体或局部的形状修改;给出了一些具体的数值实例。造型实例表明,该方法在计算机辅助几何设计中具有一定的应用价值。
Based on the analysis of the the quartic C-Bézier basis function, this paper puts forward two methods about the control shape of the quartic C-Bézier, the modify control parameterαand modify control vertex that control parameters on the role of the shape, and puts forward the control parameters adjustment methods of modification curve shape. On the other hand, based on the relations of control points and the curve shape, it establishes the algorithm of adjustment control vertex. Finally, the paper puts forward some specific numerical experiments. The modeling examples show that the method in computer aided geometric design has certain application value.

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针对C-Bézier曲线的近似降阶问题,基于遗传算法,给出了一种用n次C-Bézier曲线最小平方逼近n＋1次C-Bézier曲线的方法。该方法从最优化思想出发,把C-Bézier曲线的降阶问题转化为求解函数的优化问题,通过选择适应值函数,利用简单的循环执行复制、交叉、变异、选择求出该优化问题的最优值,从而实现了C-Bézier曲线在端点无约束和端点G0约束条件下的近似降阶逼近。实例结果表明,所提方法不仅可以获得较好的降阶效果,而且易于实现、精度高、误差计算简单,可以广泛地应用于计算机辅助设计中对曲线的近似降阶。
Aimingat C-Bézier curve of approximate degree reduction problem, a method for constructing an approximative C-Bézier curve of degree n to a C-Bézier curve of degree n+1 by genetic algorithm is provided. By means of optimization meth-ods, degree reduction of C-Bézier curves is transformed to an optimization problem, by selecting the fitness function, using a simple loop reproduction, copy process, crossover process, mutation process, selection process obtaining the optimal value of the optimization problem to achieve C-Bézier curve endpoints in the endpoint G0 unconstrained and constrained approximate reduc-tion. The experimental results illustrate that the proposed method not only has a good merging effect, but also is easy to imple-ment, has high precision and is simple for error estimation.

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地方测强曲线在回弹法检测商品混凝土抗压强度时优于国家统一曲线,针对庆阳商品混凝土的特点,采用本地区具有代表性的原材料,制作了C10、C15、C20、C25、C30、C35、C40、C45、C50、C55、C60混凝土试块,分为14、28、60、90、120d,5个龄期进行测试,利用最小二乘方法,得到了幂函数形式的回归方程。采用其作为本地区高强混凝土回弹法地方测强曲线。
The local strength curve of the commercial concrete compressive strength in the rebound method is superior to the national unification curve. In the light of the characteristics of commodity concrete in Qingyang and using the representative raw materials of the region,the concrete samples of C10、C15、C20、C25、C30、C35、C40、C45、C50、C55、C60 are made.Test is divided into five ages for 14、28、60、90、120 days.With the least squares method,we can get the regression equation of power function.it can be used as the local high strength concrete curve of the region by rebound method.

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目的建立解剖结构较为精确的下颈椎三维有限元模型并验证其有效性。方法采用正常成人颈椎CT图像建立C4-C5-C6有限元模型。在屈伸、侧弯、轴向旋转加载条件下绘制模型的力矩-位移曲线,计算曲线在实验生物力学模型所建立的力矩-位移标准差范围中所占的百分比。结果和结论建立了正常颈椎C4-C5-C6节段有限元模型,力矩-位移曲线在标准差范围中所占的百分比平均为90%。
Objective To develop and validate an anatomic detailed finite element model of the lower cervical spine. Methods The fi-nite element model of C4-C5-C6 was constructed using lower cervical spine (C4-C5-C6) CT images of a young healthy man. This model was validated against the standard deviation corridors of experimental data for normal, nondegenerated cervical spines tested in flexion and ex-tension, right and left lateral bending, and right and left axial rotation under physiological loading. Percent of load range deviation was intro-duced to measure the deviation of the model from the standard deviation corridors of experimental data. Results and Conclusion A finite el-ement model of young normal lower cervical spine has been developed and validated. The average percentage of load range was within 90%of standard deviation corridor.

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给出了一种带形状参数的三次三角Hermite插值样条曲线，具有标准三次Hermite插值样条曲线完全相同的性质。给定插值条件时，样条曲线的形状可通过改变形状参数的取值进行调控。在适当条件下，该样条曲线对应的Ferguson曲线可精确表示椭圆、抛物线等工程曲线。通过选择合适的形状参数，该插值样条曲线能达到C 2连续，而且其整体逼近效果要好于标准三次Hermite插值样条曲线。
A class of cubic trigonometric Hermite interpolating splines curves with shape parameters is presented in this paper, which inherits the same properties of the standard cubic Hermite interpolating splines. For given interpolating con-ditions, the shape of the proposed splines curves can be adjusted by changing the values of the parameters. In proper con-ditions, the corresponding Ferguson curve can be used to represent some engineering curves exactly, such as ellipse and parabola. By selecting proper shape parameters, the proposed interpolating splines curves could satisfy C 2 continuous and approximate the interpolated functions better than the standard cubic Hermite interpolating splines curves.

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热释光(TL)与线性调制光释光(LM-OSL)激发晶体的原理和方式具有很高的相似性。论文致力于通过设定一定的模拟实验条件,采用Maxima数学软件对α-Al2O3:C晶体的TL曲线和LMOSL曲线进行模拟,研究这两种释光曲线峰值的参数依赖相似性。初步研究表明,在特定的模拟实验条件下,两种释光曲线峰值的参数依赖具有一定的相似性,释光曲线峰值与n0值,加热速率q(或溢出常数f0)呈现正比例关系。
Principles and stimulate process of the Thermo -luminescence ( TL) and linear modulation OSL ( LM-OSL) Luminescence are highly similar .Using the OTOR model and the Maxima software , selecting the set of parameters of α-Al2 O3:C crystal, the similarity of the dependence of the TL curve and the LM -OSL curve of the α-Al2 O3: C crystal has been studied .Preliminary studies indicate that , under certain simulated condi-tions, the TL and LM-OSL curves of the α-Al2 O3: C crystal have certain similarities , The luminescence maximums are proportional to the filling of the traps (n0), heating rate q(or f0).

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目的：探讨冠心病患者中糖化血红蛋白(HbA1c)诊断糖尿病(DM)的理想切点及可行性。方法选择经冠脉造影确诊的冠心病患者158例,所有患者均行空腹血糖、2 h OGTT和糖化血红蛋白检测,采用受试者工作特征曲线( ROC曲线)进行判断,得到诊断DM的HbA1c值,计算最佳切点。结果158例入选的冠心病患者中,平均HbA1c为(6.27±1.04)%；诊断为正常糖耐量(NGT)37例,HbA1c为(5.32±0.08)%；糖调节受损(IGR)52例,HbA1c为(6.03±0.36)%；DM 69例,HbA1c为(6.96±1.11)%。糖代谢异常的发生率为76.6%。通过绘制ROC曲线,得到HbA1c与诊断DM 相关的临界点为6.35%,敏感性和特异性分别为67%和95%,曲线下面积为0.88(95%CI 0.823-0.935)。结论 HbA1c≥6.35%作为筛查DM切点具有较高敏感度与特异度,可作为临床DM 筛查的切点。
Objective To investigate the optimal cut-off point and feasibility of glycated hemoglobin( HbA1c) for diagnosing diabetes mellitus( DM) in patients with coronary artery diseases by coronary angiography. Methods A total of 158 patients with coronary heart diseases diagnosed by coronary angiography were included. The fasting glucose,2 h OGTT and glycosylated hemoglobin were detected in all patients. A receiver operating characteristic curve was used to calculate the optimal cut-off point of diagnosing DM by HbA1c. Re-sults The average HbA1c of 158 cases of coronary heart diseases was (6. 27 ± 1. 04)%. HbA1c was (5. 32 ± 0. 08)% in 37 cases of normal glucose tolerance(NGT),and (6. 03 ± 0. 36)% in 52 cases of impaired glucose regulation(IGR),and (6. 96 ± 1. 11)% in 69 cases of DM. The incidence of abnormal glucose metabolism was 76. 6%. The optimal cut-off point of diagnosing DM by HbA1c was 6. 35%,and the sensitivity and specificity of diagnosing DM by HbA1c were 67% and 95%

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采用C30混凝土按碳纤维体积掺量2‰进行配合比设计,制作了3个试验试件柱,对其进行水平低周往复加载,分析其在轴压比0.4、0.5、0.6下试件的滞回曲线、骨架曲线及位移延性系数;同时采用ABAQUS软件对碳纤维混凝土柱的滞回性能进行有限元分析,得到碳纤维柱的滞回曲线和应力云图。结果表明,轴压比的变化对试件滞回曲线的饱满程度影响不大,不同轴压比下试件的滞回曲线均比较饱满,没有出现捏拢现象,到达极限承载力后,曲线下降平缓;随着轴压比的增大,试件的极限承载力降低,所对应的极限位移和延性系数均减小。采用ABAQUS软件模拟得到的曲线与试验所得曲线吻合较好。
Three specimens of carbon fiber reinforced concrete columns with C30 concrete strength grade and 2‰carbon fiber are tested to study their hysteresis curve, skeleton curve and displacement ductility coefficient when the axial compressive ratios are 0.4, 0.5 and 0.6. And carbon fiber concrete columns are analyzed by using the finite element soft-ware ABAQUS, the hysteretic curve and stress nephogram of the columns are achieved. The results show that the change of axial compression ratio has little influence on the full extent of the hysteretic curves. The hysteretic curves under dif-ferent axial compression ratios are full without significant pinch phenomenon. When the limit bearing capacity of the columns is reached, the skeleton curve decreases slowly. With the increase of axial load ratio, the ultimate bearing capac-ity and limit displacement decrease. The simulation curve and experimental curve are in good agreement which proved the rationality of simulation.

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介绍一种判断C/C编织复合材料损伤程度的新方法——使用撞击计数和振铃计数在结构静加载过程中的相关曲线,判断其损伤程度的严重性。通过监测1组C/C复合材料结构的静力强度试验,发现声发射中撞击计数和振铃计数的相关增长曲线与结构的损伤程度相关:该曲线脱离之前的良好线性关系,突然出现明显拐点,意味着较严重损伤的发生。此时载荷与破坏载荷的比值,对于一定结构比较稳定。该方法可以比较准确有效地预警复合材料结构的破坏,并给出破坏载荷的估计值;这个现象对分析解释复合材料结构损伤场的发展也有一定的启示。
A new method to evaluate the damage extent of composite material structure is presented: determine the severity of damage extent from the relative curve of hits and counts of AE, attained from static load procedure of structure. We find that the ascending curve of counts and hits is related to the damage extent of structure by monitoring a series of static load test of C/C composite structure: the curve deviate from its prior linearity and deflection point appeared in a sudden when more severe damage occurred;and the ratio of load at this time to the final fracture load is steady for a certain structure. This method could early warn the failure of composite structure effectively and estimate the fracture load. This phenomenon could also provide some suggestion to interpret the evolution of damage field of composite structure.

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