Thermal Expansion Coefficients of Thin Crystal Films

The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.

The “Dead Universe” Theory: Natural Separation of Galaxies Driven by the Remnants of a Supermassive Dead Universe

This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This perspective challenges the conventional Big Bang theory, particularly concerning dark matter, the expansion of the universe, and the interpretation of phenomena such as gravitational waves.

On a Fractal Version of Witten’s M-Theory

Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluz-Klein （KK） theory have been applied in the domain of cosmology. These equations are solved for a fiat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor＇s expansion of cosmological function, A（t）, up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.

Possible Evolutionary Models in the Initially Hydride Earth Theory

A modern view of the properties of chemical elements has confirmed the theory of the hot origin of the Earth. The next step in developing this theory was the hypothesis of the initial hydride Earth. In this work, we attempted to find additional evidence for this hypothesis and show additional effects that flow from it. The effect of the physical properties of atoms and ions on their behavior during the formation of the Earth was studied. The maximum contribution to the distribution of elements was made by those elements whose content in the original protoplanets of the disk was the maximum. Correlation dependence is obtained, which allows one to calculate the distribution of elements in the protoplanetary disk. It was shown that hydrogen was the main element in the proto substance located in the zone of the Earth’s formation. In this case, various chemical compounds formed, most represented by hydrogen compounds—hydrides. Since the pressure inside the Earth is 375 GPa, this factor forces the chemical compounds to adopt stoichiometry and structure that would not be available in atmospheric conditions. It is shown that many chemical elements at high pressure in a hydrogen medium form simple hydrides and super hydrides—polyhydrides with high hydrogen content. Pressure leads to a higher density of matter inside the planet. Given the possibility of forming polyhydrides, there is the possibility of binding the initially available hydrogen in an amount that can reach 49.3 mole%. Young Earth could contain about 10.7 mass% of hydrogen in hydrides, polyhydrides, and adsorbed form is almost twice higher than previous estimates. This fact additionally confirms the theory of the original hydride Earth. In hydrides, the occurrence of the phenomenon of superconductivity was discovered. Polyhydrides were shown as potential superconductors with a high critical temperature above 200 K. We, based on these data, hypothesized the presence of superconducting properties in the Earth’s core, which explains the presence of a magnetic field in the Earth, as well as the unevenness and instability of this field and the possibility of migration of the Earth’s poles. The fact that the Earth has a hydroid core causes its change in time due to the instability of hydrides. Arranged several possible models of the destruction of the Earth’s core. The calculations showed that both models give close results. These results give predictions that can be measured. The proposed models also made it possible to estimate the initial size of the Earth. Possible ways of further testing the hypothesis of the initial hydride Earth is shown.

基于Taylor级数展开定理的高阶FDTD的色散分析

时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具。而 Taylor 级数展开定理是构造差分格式的一种重要方法,例如 Yee 格式采用二阶 Taylor 格式,Fang 格式采用四阶 Taylor 格式。本文借助于采样定理,详细分析了不同阶 Taylor 中心差分格式的谱特性以及计算误差,并将任意阶 Taylor 中心差分格式用于数值求解麦克斯韦方程中,严格导出了稳定性条件和数值色散关系的表达式,引入了新的误差定义来衡量算法的好坏。详细地研究了 Courant 数、网格分辨率 CPW 和网格长度比率等因素对于数值色散误差的影响,为基于 Taylor 差分格式的 FDTD 算法的研究提供了有用的参考。

基于改进D-S的高速公路改扩建交通安全风险评估模型

为提高高速公路改扩建工程交通安全风险评估结果的确定性和准确性,建立了基于改进D-S证据理论的相关风险评估模型。首先建立包含24个影响因素的三层级评估指标体系;然后利用云模型(Cloud Model,CM)求出定性指标的基本信度赋值(Basic Probability Assignment,BPA),利用高斯隶属度函数求出定量指标BPA;接着,通过层次分析法确定各评估指标的权重,进而对各指标BPA进行加权;利用D-S证据理论融合加权后的BPA,归一化处理后得到改扩建工程交通安全风险状态评估结果。最后,为验证模型的准确性,选取沪陕高速公路平潮至广陵段高速公路改扩建工程作为实例进行交通安全风险评估。评估结果显示,实例工程的低风险水平隶属度最大,为0.6615,表明该实例总体处于低风险水平,与现有资料和现实情况吻合。同时发现,基于CM、AHP及D-S证据理论的评估模型对各评估指标进行量化、加权、融合后所得到的风险等级隶属度和不确定性有所区别,能更均衡地表示风险的隶属度,量化后的安全风险状态评估结果具有更好的准确性,解决了指标体系中模糊定性指标难以量化表征及指标差异化权重赋值的难题。

非齐次Schrdinger方程的交替隐式格式

以Taylor展开为基本工具,研究了非齐次多维Schrdinger方程的交替方向隐格式.此格式在时空方向均具有2阶精度,而且所需求解的代数方程组的阶数与1维问题一样,具有经济、实用、易于模块化编程实现等优点.数值实验主要检验了数值格式长时间的模拟能力、离散电荷随时间演化关系等.

Dark Matter Creation and Anti-Gravity Acceleration of the Expanding Universe

Dark matter is identified as negative relative energy between quarks in proton and is generated in cold hydrogen gas with pressure gradient in gravitational field. Positive relative energy PRE can be generated between quarks in protons in cold hydrogen gas in outskirts of the universe. The mechanisms for such creation of dark matter and PRE are reviewed and updated in greater detail and clearer manner. The so-generated dark matter in a galaxy can account for the galaxy’s rotation curve. Star formation in this galaxy uses up the hydrogen atoms and thereby reduces its dark matter content. Dark matter created in intergalactic hydrogen gas can form filaments. In a hypothetical model of the universe, a hydrogen atom with a small amount of negative relative energy or dark matter at the outskirts of this universe can via collisions with other atoms turn into one with a small positive relative energy PRE. Once such a sign change takes place, gravitational attraction switches to anti-gravity repulsion unopposed by any pressure gradient. This leads to a “run away” hydrogen atom moving away from the mass center of the universe and provides a basic mechanism for the accelerating expansion of the universe. This theoretical expansion and the measured redshift data are both compatible with the conception of an acceleratingly expanding universe and complement each other. But they cannot verify each other directly because the present model has been constructed for purposes different from those of the measurements. But it can be shown that both approaches do support each other qualitatively under certain circumstances for small velocities. Dark matter and PRE in the present model are not foreign objects like WIMPs and dark energy-cosmological constant but can only be created in cold hydrogen gas in gravitational field. To achieve this, infrequent collisions among the hydrogen atoms must take place. Dark matter was created first and can eventually later evolve into PRE in the outskirts of the universe and in the intergalactic void. Dark matter and PRE will disappear if the hydrogen atom carrying them becomes ionized as in stars.

Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos

The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.

An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.

Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.

A Combined Heterotic String and Kähler Manifold Elucidation of Ordinary Energy,Dark Matter,Olbers’s Paradox and Pure Dark Energy Density of the Cosmos

We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.

定积分在两点展开的渐近公式

对于具有m+n阶连续导数的被积函数的定积分,通过多次分部积分给出了在积分上限和积分下限两点处同时展开的定积分的渐近展开式,其余项类似于Taylor公式的积分型余项,这种展开式可看作是Taylor公式的一种推广.被积函数在积分上下限处的值有不同情形,展开式也会随之变化而具有多种形式.通过分析与举例也发现这种展开式的近似计算优于Taylor公式的近似计算,而且在某些积分不等式的证明中也体现了其快捷方便的优点.

利用叠前AVO反演预测砂岩储层有效压力

求取垂直上覆压力和孔隙压力估计有效压力的方法,由于常规的利用声波时差拟合的正常压实趋势曲线的精度较低,导致地层压力预测精度较低;岩石物理方法仅停留在实验阶段或依赖经验模型,在理论上无法准确预测有效压力;孔隙空间刚度理论为考虑压力因素的岩石物理建模提供了新思路,但有效压力研究仅停留在岩石物理建模阶段,缺少由地震资料直接稳定预测有效压力的手段。为了由地震数据直接预测有效压力,提出了利用叠前AVO反演预测砂岩储层有效压力的方法。首先,假设干岩石骨架的弹性模量比为定值,基于孔隙空间刚度理论构建了剪切模量与有效压力的岩石物理关系;其次,采用泰勒展开得到弹性参数与物性参数的线性转换关系;再次,推导有效压力、孔隙度、流体模量、基质剪切模量和密度的反射系数方程,并构建基于贝叶斯理论的叠前地震反演流程。模型测试与实际资料应用表明,即使在低信噪比情况下,所提方法依然能稳定预测地层有效压力。

一种改进的无线定位算法

Taylor级数展开法和Chan算法是两种性能优良的利用电波到达时间差(TDOA)的定位算法,前者简单实用,但是其缺点是对初值比较敏感；后者在视距(LOS)传播环境下有较高的定位精度,二者结合可以大大提高定位的精度。但是在非视距(NLOS)传播环境下Chan算法精度会受到较大的影响,从而影响到Taylor级数展开法的定位精度。本文根据NLOS传播环境下附加传播时延和均方根时延扩展的统计特性,对NLOS误差的均值和方差进行估计,对TDOA测量值进行修正,采用Chan算法计算初值,再利用Taylor级数展开法进行定位,并与其它两种基于Taylor级数展开法的定位方法结果进行了比较。仿真结果表明,该算法能够提高NLOS传播环境下的定位精度,性能优于另外两种基于Taylor级数展开法的定位方法。

分数阶Bagley-Torvik方程的近似解

将泰勒展开法应用到分数阶Bagley-Torvik方程,同时把方程分数阶取值范围由(0,1)推广到(1,2),使此方程更接近实际背景。最后,验证了该方法的高效性。

硫化锂分子的分析势能函数和光谱

应用密度泛函理论的B3LYP方法和6-311++g(d,p)基组,研究Li_2、Li S和Li_2S分子的基态构型.结果表明它们的基电子态分别为X^1Σ_g^+、X^2Π和X^1Σ_g^+.通过非线性曲线拟合,得到基态Li S和Li_2分子的4参数MurrellSorbie分析势能函数,计算它们的光谱参数和力常数.基于多体项展式理论得到了基态Li_2S分子的单重态势能面的分析函数.利用得到的分析势能函数重构基态单重Li_2S分子的旋转图、伸缩图和旋转伸缩图,准确地再现了Li_2S分子的静态特征,如平衡结构,最低能量,合理反应通道.从等值势能面图看出,反应Li+S+Li→Li_2S是一个无阈值反应.S原子攻击Li_2分子的反应通道上,有一个过渡态.Li原子攻击Li S分子通道上也有一个过渡态.

绣花机失步现象的分析与研究

分析了绣花机在刺绣过程中出现偏差的可能原因。首先采用圆弧差补的算法来反映加工偏差,通过对偏差的修正,取得了初步的图形优化结果。其次,针对摩擦力、负载力以及其它诸多外界因素引起的不稳定干扰,采用了细分步距角结合圆弧插补的方法来解决丢失步的问题,并且基于三次样条函数对步进电机控制量和步距角之间的关系进行曲线拟合。最后利用连续函数的泰勒展开式特性,通过灵活修改控制量来修正步距角与理论值之间的偏差,使得步进电机的步矩角更加均匀,在实践过程中取得了良好的效果。

压力容器非概率可靠性设计方法

为解决压力容器概率可靠性设计分布函数难以确定的问题,采用区间理论,将有边界限制的压力容器筒体内径、应力及载荷等参数用区间变量来描述。通过泰勒级数展开、中心复合实验设计以及顶点法3种方法对压力容器进行非概率可靠性设计。结果表明:常规压力容器设计结果比较保守,采用非概率可靠性设计能够获得轻量化结果。由此,引入区间模型的压力容器可靠性设计,降低了对原始数据的要求,优化了设计结果。