Research and Application of a Multi-Field Co-Simulation Data Extraction Method Based on Adaptive Infinitesimal Element

Regarding the spatial profile extraction method of a multi-field co-simulation dataset,different extraction directions,locations,and numbers of profileswill greatly affect the representativeness and integrity of data.In this study,a multi-field co-simulation data extractionmethod based on adaptive infinitesimal elements is proposed.Themultifield co-simulation dataset based on related infinitesimal elements is constructed,and the candidate directions of data profile extraction undergo dimension reduction by principal component analysis to determine the direction of data extraction.Based on the fireworks algorithm,the data profile with optimal representativeness is searched adaptively in different data extraction intervals to realize the adaptive calculation of data extraction micro-step length.The multi-field co-simulation data extraction process based on adaptive microelement is established and applied to the data extraction process of the multi-field co-simulation dataset of the sintering furnace.Compared with traditional data extraction methods for multi-field co-simulation,the approximate model constructed by the data extracted from the proposed method has higher construction efficiency.Meanwhile,the relative maximum absolute error,root mean square error,and coefficient of determination of the approximationmodel are better than those of the approximation model constructed by the data extracted from traditional methods,indicating higher accuracy,it is verified that the proposed method demonstrates sound adaptability and extraction efficiency.

Infinitesimal dividing modeling method for dual suppliers inventory model with random lead times

As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.

Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System

It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.

ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS

In this paper, we consider the infinitesimal I- and Il-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E-3 Go the submanifolds immersed in a space form of constant curvature.

RELATIONS BETWEEN PERFORMANCE POTENTIALS AND INFINITESIMAL REALIZATION FACTORS IN CLOSED QUEUEING NETWORKS

In this paper,the concept of the infinitesimal realization factor is extended to the parameter dependent performance functions in closed queueing networks.Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed.This provides a united framework for both IPA and non IPA approaches.Finally,another physical meaning of the service rate is given.

From Braided Infinitesimal Bialgebras to Braided Lie Bialgebras

The present paper is a continuation of [1], where we considered braided infinitesimal Hopf algebras (i.e., infinitesimal Hopf algebras in the Yetter-Drin feld category for any Hopf algebra H), and constructed their Drinfeld double as a generalization of Aguiar’s result. In this paper we mainly investigate the necessary and sufficient condition for a braided infinitesimal bialgebra to be a braided Lie bialgebra (i.e., a Lie bialgebra in the category ).

Influence of Infinitesimal Neglected Effects by Current Theory of Gravitation and Experiments on the Stability of the Universe

From the hypotheses compatible with microphysics theory, this paper establishes a new theoretical model of static universal gravitation and deduces new formula of the theory of universal gravitation. In a first order approximation, the new formula shows the inverse-square law consistent with Newton formula, which would indicate that the new theory is consistent with the experimental results that can be reasonably explained by the current theory of gravitation. The parameters and higher order terms among the coefficients of this paper reveal the numerous infinitesimal neglected effects by current theory and experiments. In the first order approximation, the meanings of the physical parameters included in coefficients are analyzed and the infinitesimal neglected effects are applied in the study of the stability of the universe, which overcomes the difficulty of singularity in the cosmology of Newton, Einstein, etc., and concludes that the boundary of universe is unlimited, without any need of the hypothesis that the universe starts off with the big bang. Therefore, this paper establishes a harmonious and ingenious relationship between microphysics and macrophysics theories. In addition, through the analysis of the formula derived from the theory of this paper, it is found that: in general, the gravitational constant is not always a constant in the gravitation formula requiring high precision;from the perspective of the interaction of field quantum, the acting force may not be equal to counter-acting force under the interaction of indirect contact;the gravity process is an exothermic process;in the gravitational process, annihilation effects may exist amongst gravitons;reciprocal translation may exist amongst fundamental forces.

A Theorem on Infinitesimal I-isometry of Surfaces Immersed in a Space with Constant Curvature

In this paper we discuss the infinitesimal I-isometric de formations of surfaces immersed in a space with constant curvature. We obtain a sufficient condition for the de formation vector field to be zero vector field which is generalization of the results in [1] and [2].

基于塑性元件微元化的重塑黄土黏弹塑性本构模型

基于塑性元件微元化和无穷级数的思想,通过加、卸载条件的三轴蠕变试验建模并通过动力三轴试验验证,建立了重塑黄土的黏弹塑性本构模型,并获得了相应的参数指标。研究表明,该模型可以很好地描述重塑黄土的蠕变、静力和动力特性,且能更加合理地解释卸载条件下回弹曲线的变化特征。塑性元件微元化的处理方法弥补了以往黏弹塑性本构模型中塑性变形不易描述的缺点,相比其他的黏弹塑性本构模型,该模型应用更加简单且适用范围更广。

定积分微元法的教学探析与思考

本着教育数学的思路,结合分析和比较三种微元法观点探析定积分微元法的主要思想,总结出定积分微元法的使用特点及判定方法,并运用微元分析法解决曲边扇形面积和变力对质点的冲量两个问题,该方法类似可推广到其他几何、物理及经济问题.

基于微元法的偏心起爆战斗部破片初速计算方法

破片在目标方向上的初速分布是评估定向战斗部威力的重要因素之一,为此对偏心双线起爆下战斗部定向侧全域破片的初速计算方法以及相较于中心起爆的动能增益进行了研究。基于微元思想推导了定向侧周向不同位置处破片初速的计算方法,开展了战斗部静爆试验,并将实验结果与理论计算进行对比,同时结合战斗部数值模拟结果对轴向速度修正函数进行了拟合,依据现有研究对算法普适性进行了验证。结果表明:所提出公式适用于偏心双线起爆战斗部,理论计算与试验结果间的误差不超过4.8%,计算结果符合实际情况;拟合所得修正函数可对轴向不同方位破片的飞散初速进行预估;在战斗部参数变化时算法仍具有较好的普适性,计算误差小于7.11%;与中心起爆相比,采用夹角为60°的偏心双线起爆模式可使定向侧中心-30°~30°范围内破片总动能增加34.9%。

地基激光雷达单木树冠体积提取球坐标积分法

树冠体积是地表生态监测研究的关键因子,激光点云可精细描述单木空间形态,为树冠体积提取提供了数据基础,但现有的激光点云单木树冠提取方法存在参数敏感、自动化程度不高等不足。文章在分析单木三维空间形态结构的基础上,提出了一种基于地基激光点云数据的单木树冠体积提取球坐标积分法。首先,根据激光点云高程分布特性,采用可视高程阈值分割得到树冠点;然后,将激光点云投影至三维球坐标空间并进行四棱锥形微元分割;最后,利用三维球坐标积分确定树冠体积。选择6种不同类型的单木激光点云数据进行试验,结果表明:文章方法能较好地顾及树冠形态、点云密度等因素,单木树冠体积提取绝对误差绝对值最大值为2.33 m^(3),相对误差最大值为3.40%,相比已有方法具有树冠提取精度高、稳定性好的优势。该研究对激光点云林木参数提取具有重要的参考价值。

等价无穷小量代换求复合函数极限的拓展

分析探讨了复合函数中内外函数都为等价无穷小量时求函数极限的问题,得到了相关定理,拓展了应用等价无穷小量代换求复合函数极限的相关结论。

广义导数及其在极值问题中的应用

首先,将经典的导数概念推广到广义导数,通过研究广义导数的性质并结合等价无穷小的相关结论给出广义导数的简便计算方法;其次,引入导数指标的概念,并证明它是同阶无穷小等价关系的完全不变量;最后,将广义导数与导数指标应用到函数极值问题中,并给出极值的一个充分必要条件.

高等数学中无穷小量的相关概念解析及应用

通过对无穷小认识的曲折历程的叙述揭示了无穷小蕴含的哲学思辨色彩,从无穷小阶数比较的角度阐释了一元函数导数与微分的本质与联系,利用泰勒公式比较无穷小的阶数并解释等价无穷小的实质,指出等价无穷小替换的使用错误根源在于用于替换的泰勒多项式精度达不到所需要求,最后给出了无穷小比较在极限审敛法中的应用。

Green公式的微元法证明

以微元法为工具,将一般情形转化为“特殊多边形”区域的情形,然后利用矩形划分处理这种特殊情形;同时,给出这两步的误差估计,从而严格证明Green公式,并加深对公式的理解.

等价无穷小在高等数学中的应用

鉴于职业院校学生数学基础,在求解极限和无穷级数等方面的问题存在较大难度,本文讨论等价无穷小在求复杂函数的极限、判别无穷级数的敛散性这两方面的应用,将帮助学生更好地解决极限和级数方面的一些问题.

多策略检视问题设计 确保试题命制质量——由一道错题引发的思考

在命题实践中,一味求新求异,致使试题所考查的知识点超出中学物理范畴,难以达到检测学生核心素养的发展过程与现有水平的目的.以一个考查连接体的经典错题为例,尝试采用微元法、求导法、极坐标法及Origin绘图4种策略厘清连接体中加速度关联情景,剖析该题错误成因,分析相同知识点在高考题中应如何设问,以规避错误的发生.希望引起一线命题者的共鸣,以此促进命题质量的提升.

高等数学课程融入课程思政的教学探索——以无穷小量为例

本文以高等数学中的一个重要概念——无穷小量为例,论述在课程教学过程中融入课程思政的方法与具体实施过程.在训练学生数学思维和方法的基础上,提高学生的科学思维和实践能力,培育学生的唯物史观、创新精神、爱国情操、美学能力等,实现对学生更高层次的价值塑造,践行高校“立德树人”的育人理念.