Unlike the literature, in this study, composite materials containing triple-walled nanotube are investigated in the scope of the piecewise homogeneous body model by using of geometric non-linear exact equations of the 3-D theory of elasticity. 与文献不同的是，本研究利用三维弹性理论的几何非线性精确方程，在分段均质体模型范围内研究了含有三壁纳米管的复合材料。

Normal stress distribution in infinite elastic matrix with a locally curved triple-walled carbon nanotube

In this model, it is used the 3-D geometrically non-linear exact equations of viscoelasticity theory. 在这个模型中，它使用了粘弹性理论的 3-D 几何非线性精确方程。

On internal stability loss of a row unidirected periodically located fibers in the visco-elastic matrix

In particular, we show that this manifestly causal approach leads to novel one-loop exact equations for fully dressed correlation functions. 特别是，我们表明，这种明显的因果方法导致了新的单环精确方程，用于完全修饰的相关函数。

Flowing with the temporal renormalization group

The result are novel one-loop exact equations for fully dressed correlation functions. 结果是用于完全修饰的相关函数的新颖的单环精确方程。

A Temporal Functional Renormalisation Group Approach to Non-Perturbative Quantum Dynamics

A form of <inline-formula><tex-math notation="LaTeX">$\boldsymbol {\alpha }$</tex-math></inline-formula>-invariance is proven for a class of fuzzy numbers (FNs) and exact equations for random variable generators of some well-known singleton-core FNs are provided. <inline-formula><tex-math notation="LaTeX">$\boldsymbol {\alpha }$</tex-math></inline-formula> 的一种形式证明了一类模糊数（FN ) 并提供了一些著名的单核 FN 的随机变量生成器的精确方程。

Fuzzy Random Variable Generation Using $\alpha$-Cuts

Coherent or exact equations of motion for a conservative post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. 保守的后牛顿拉格朗日形式主义的相干或精确运动方程是没有任何项截断的欧拉-拉格朗日方程。

Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Exact equations for the Greens functions are obtained by generalizing Gor'kov's equations to include extremely strong local repulsion between electrons of opposite spin. 格林函数的精确方程是通过将 Gor'kov 方程推广到包括相反自旋电子之间极强的局部排斥来获得的。

Extremely correlated superconductors

We present the exact equations to design a stigmatic singlet that meets the Herschel’s condition. 我们提出了精确的方程来设计满足赫歇尔条件的柱头单线态。

Exact equations to design a stigmatic singlet that meets the Herschel’s condition

We numerically resolve the exact equations of motions to investigate the orbital motion of thousands of test particles within and near the domain of the 7/6, 14/15, 10/11 mean-motion resonances of Aegaeon, Methone, and Anthe with Mimas, respectively. 我们通过数值求解精确的运动方程，以研究 Aegaeon、Methone 和 Anthe 与 Mimas 的 7/6、14/15、10/11 平均运动共振域内和附近的数千个测试粒子的轨道运动，分别。

Dynamical stability in the vicinity of Saturnian small moons: the cases of Aegaeon, Methone, Anthe, and Pallene

We present the exact equations for designing a stigmatic singlet lens that meets Abbe’s sine condition for each ray. 我们提出了用于设计满足每条光线的阿贝正弦条件的散光单重透镜的精确方程。

Exact equations for stigmatic singlet design meeting the Abbe sine condition

We compare these with those obtained in numerical solutions of the exact equations. 我们将这些与在精确方程的数值解中获得的那些进行比较。

Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

The optical constants and the optical energy gap were extracted from SE by constructing an ellipsometric optical model, while the optical constants were calculated from SP by using Murmann's exact equations. 通过构建椭偏光学模型从SE中提取光学常数和光学能隙，而使用Murmann精确方程从SP中计算光学常数。

Optical properties upon ZnS film thickness in ZnS/ITO/glass multilayer films by ellipsometric and spectrophotometric investigations for solar cell and optoelectronic applications

We present a mechanism for the generation of extreme vertical drafts and vorticity enhancements which follows from the exact equations for field gradients. 我们提出了一种产生极端垂直气流和涡度增强的机制，该机制来自场梯度的精确方程。

Connecting large-scale velocity and temperature bursts with small-scale intermittency in stratified turbulence

A form of α-invariance is proven for a class of fuzzy numbers and exact equations for random variable generators of some well known singleton-core fuzzy numbers are provided. 为一类模糊数证明了一种形式的α不变性，并提供了一些众所周知的单核模糊数的随机变量生成器的精确方程。

Fuzzy random variable generation using α-cuts

Exact equations of motion in terms of the so-called conformal variables are used. 使用根据所谓保形变量的精确运动方程。

Waves over Curved Bottom: The Method of Composite Conformal Mapping

10.1088/1742-6596/1253/1/012012

The exact equations of the thermoluminescence (TL) glow curve deconvolution that describe the intensity of a single TL glow peak of different order kinetics, which are obtained from the one trap-one recombination (OTOR) level model, are considered. 考虑了从单阱一重组 (OTOR) 水平模型获得的描述不同阶动力学的单个 TL 发光峰强度的热致发光 (TL) 辉光曲线反卷积的精确方程。

New handling of thermoluminescence glow curve deconvolution expressions for different kinetic orders based on OTOR model

The exact equations of motion of the theory of linear viscoelasticity are used and the complex dispersion equation is obtained for an arbitrary type of hereditary operator of the viscoelastic materials. 使用线性粘弹性理论的精确运动方程，得到任意类型的粘弹性材料遗传算子的复色散方程。

On attenuation of the seismic Rayleigh waves propagating in an elastic crustal layer over viscoelastic mantle

We derive the exact equations for bound-state energy eigenvalues and construct accurate approximations for the energy spectrum. 我们推导出束缚态能量特征值的精确方程，并为能谱构建精确的近似值。

Exact solution of the 1D Dirac equation for the inverse-square-root potential 1 / x $1/\sqrt{x}$

As a part of validating the theory, numerical integration of the exact equations of motion of the interacting many-drop system has been carried out. 作为验证理论的一部分，已经对相互作用的多点系统的精确运动方程进行了数值积分。

Self-consistent theory of spatial distribution of an assembly of charged drops in an electrodynamic balance

However, the applicability of this framework to empirical data has been limited because equilibrium dynamics of populations within communities are seldom observed in nature and exact equations for community dynamics are rarely known. 然而，该框架对经验数据的适用性受到限制，因为在自然界中很少观察到社区内种群的平衡动态，并且很少知道社区动态的精确方程。

Non-parametric estimation of the structural stability of non-equilibrium community dynamics

The exact equations for these vectors are also provided and depend on the second and the fourth order statistical moments of the sample sequence only. 还提供了这些向量的精确方程，它们仅取决于样本序列的二阶和四阶统计矩。

The unsupervised optimum linear finite length filter for fourth order wide sense stationary single output systems

Here, we provide a first demonstration of a self-consistent solution of the exact equations, with a preliminary analysis of their stability and convergence properties. 在这里，我们首次演示了精确方程的自洽解，并初步分析了它们的稳定性和收敛性。

On the numerical solution of the exact factorization equations.

At the least, the exact equations should be used to check results obtained by the WGA in wavelength regions of interest. 至少，应该使用精确的方程来检查 WGA 在感兴趣的波长区域中获得的结果。

Failure of the Weakly Guiding Approximation for Few-Mode Fiber Index Profiles

We compare the efficient calculation of weak lens optical scalars with the exact equations; finding an excellent agreement. 我们将弱透镜光学标量的有效计算与精确方程进行比较；找到一个很好的协议。

Efficient gravitational lens optical scalars calculation of black holes with angular momentum

By solving the exact equations of motion, including the dissipative effects and the mutual gravitational perturbations, we investigate the configuration of the system soon after the guiding satellite is disrupted when crossing the Roche limit with the central planet during its orbital decay. 通过求解精确的运动方程，包括耗散效应和相互引力扰动，我们研究了在引导卫星在轨道衰减期间与中央行星越过罗氏极限时被破坏后不久的系统配置。

Primordial migration of co-orbital satellites as a mechanism for the horseshoe orbit of Janus-Epimetheus

Exact equations for critical amplitudes at different frequencies of the pump field are obtained in the resonance approximation. 在共振近似中获得了泵场不同频率下临界振幅的精确方程。

Parallel pumping of spin waves in a ferromagnet revisited