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.

Comparison of the time-domain electromagnetic field from an infinitesimal point charge and dipole source

An electromagnetic field is generated through the accelerating movement of two equal but opposite charges of a single dipole. An electromagnetic field can also be generated by a time-varying infinitesimal point charge. In this study, a comparison between the electromagnetic fields of an infinitesimal point charge and a dipole has been presented. First, the time-domain potential function of a point source in a 3D conductive medium is derived. Then the electric and magnetic fields in a 3D homogeneous lossless space are derived via the relation between the potential and field. The field differences between the infinitesimal point charge and the dipole in the step-off time, far-source, and near-source zones are analyzed, and the accuracy of the solutions from these sources is investigated. It is also shown that the field of the infinitesimal point charge in the near-source zone is different from that of the dipole, whereas the far-source zone fields of these two sources are identical. The comparison of real and simulated data shows that the infinitesimal point charge represents the real source better than the divole source.

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].

Infinitesimal Methods in the Works of Thabit ibn Qurra and L, Euler in Spherical Trigonometry

In one of his astronomical works the prominent arabic medieval scientists Thabit ibn Qurra （836-901） studied the visible motion of the Sun and found the points, where its velocity is maximum or minimum. He also lbund the points on the ecliptic, where this velocity is equal to the average velocity of the Sun over all the ecliptic. For this purpose he used the idea of infinitely small arcs and their ratios in different points of the circle. The great scientist Leonard Euler （1707-1783） introduced in his works on spherical trigonometry the line-element ds of the surface of the sphere, i.e. the differential of the arc length. He constructed the spherical trigonometry as an inner geometry on the surface of the sphere. He replaced the trigonometry lines, which were in use befbre him, by trigonometric functions.

ISOMETRY AND PHASE-ISOMETRY OF NON-ARCHIMEDEAN NORMED SPACES

In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator.

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.

探究微积分——让知识成为智慧

沿着历史脉络,准确把握微积分概念,领悟微积分蕴含的丰富智慧.数学智慧可以充实读者的精神世界,促进学生的心智成长,对他们的思维方式和世界观产生积极影响.在培养逻辑思维能力的同时,重视直觉思维能力,促进创新能力的培养.

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。

“1-u(x)” 型无穷小的等价无穷小

本文从考研数学和竞赛数学中频繁出现的“1-u(x)”型无穷小量的极限问题入手,基于无穷小量等价与相等的关系定理,给出“拆项配凑法”和“对数拆分法”两种等价无穷小分析方案,简化了相应问题的极限计算过程,丰富和发展了等价无穷小的应用方法.

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。

力学与数理融合——浅谈相似性解方法

基于教学实践,针对半无穷大空间Stokes第一问题,讨论了相似性解方法与微分代数领域之间的联系。阐明了初边值条件与微分方程的李群无穷小对称性相容是相似性解存在的必要条件,并首次给出了相似性解方法能使偏微分方程化为常微分方程的严格证明。本文旨在展现热-流科学相关课程引入现代数理观点的必要性,引导学生关注各类近似方法背后的物理思想,提升学生把握核心物理图像、构建合理数学语言和建模求解具体问题的能力。

Non-Archimedean空间中三次方程的稳定性

研究了三次方程Ef(x,y):=f(mx+y)+f(mx-y)-mf(x+y)-mf(x-y)-2m(m2-1)f(x)=0在non-Archimedean空间中的稳定性问题,其中m为任一实数且m≠1且m≠0.证明了如果G为一赋范空间,X为一完备的non-Archimedean空间.f:G→X是一个映射,δ>0,使得当x,y∈G时,有‖Ef(x,y)‖≤δ(ρ(‖x‖3)+ρ(‖y‖3)),其中ρ:[0,+∞)→[0,+∞)满足ρ(|m|t)≤ρ(|m|)ρ(t)及ρ(|m|)<|m|,那么存在惟一三次映射Q:G→X,使得‖f(x)-Q(x)‖≤δ2|m|3ρ(‖x‖3)(x∈G).

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。