Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.     

The World Is Not a Theorem

The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, exploit novel opportunities that are created in this continuous blooming dynamics. Affordances play a fundamental role in the evolution of the biosphere, for organisms can exploit them for new morphological and behavioral adaptations achieved by heritable variations and selection. This way, the opportunities offered by affordances are then actualized as ever novel adaptations. In this paper, we maintain that affordances elude a formalization that relies on set theory: we argue that it is not possible to apply set theory to affordances; therefore, we cannot devise a set-based mathematical theory to deduce the diachronic evolution of the biosphere.     

关于可拓集合的运算

根据蔡文提出的可拓集合的新定义,给出了可拓集合的包含、并、交、非运算的新定义,并讨论了有关运算性质,进而获得可拓域与稳定域的几个交并运算结果.     

Completeness of Gaussian orbital and geminal basis sets for linear molecules in L2 and in the first and second Sobolev spaces

Completeness theorems for Gaussian orbital and geminal basis sets of axial symmetry are proved in the space L² of square integrable functions and in the first and second Sobolev spaces H¹ and H². © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 357–384, 1998     

Cu50Ni50合金快速凝固的分子动力学模拟

采用分子动力学模拟的方法研究了Cu₅₀Ni₅₀合金在不同冷却速度下的凝固过程,利用均方位移、径向分布函数和结构可视化等方法分析其微观结构.并对凝固模型进行拉伸模拟,通过应力应变曲线和直观结构变化分析其性能.研究表明：冷却速度对Cu₅₀Ni₅₀合金凝固形成的结构有较大影响,随着冷却速度的升高,凝固形成的结构中晶体含量减少,在较低的冷却速度下,如冷却1×10¹²K/s时,Cu₅₀Ni₅₀合金凝固形成晶体结构;在较高的冷却速度下,如1×10¹⁴K/s时,Cu₅₀Ni₅₀合金凝固形成非晶体结构,且非晶Cu₅₀Ni₅₀合金的抗拉性能要优于晶体Cu₅₀Ni₅₀合金.     

Compatibility of correlation‐consistent basis sets with a hybrid Hartree–Fock/density functional method

The present study examines the feasibility of combining the correlation‐consistent basis sets developed by Dunning and coworkers with the hybrid Hartree–Fock/density functional method B3LYP. Furthermore, extrapolation to the complete basis set (CBS) limit minimizes errors due to the presence of an incomplete basis set and can act as a rigorous test of the limitations of the B3LYP method. Equilibrium geometries, energies, and harmonic vibrational frequencies were determined for a series of well‐studied, yet computationally challenging, small inorganics and their respective ions. The results were then extrapolated to the CBS limit, where applicable, and compared to experiment. It was found that a union between the hybrid Hartree–Fock/density functional B3LYP method and Dunning's augmented correlation‐consistent basis sets gave results that were comparable to molecular orbital methods that explicitly account for electron correlation. Furthermore, the minimum basis set necessary to attain reasonable results for the systems studied was aug‐cc‐pVTZ. Upgrading to the aug‐cc‐pVQZ level and subsequent extrapolation to the CBS limit further improved the overall agreement with the experiment. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 207–216, 1999     

Dynamic hyperpolarizabilities in Møller–Plesset perturbation theory

As a formulation for calculating the dynamic polarizabilities and hyperpolarizabilities, two different types of the time‐dependent Møller–Plesset perturbation theory (MPPT) are presented: the MPPT in the quasienergy derivative method (QED–MPPT) and the MPPT in the energylike derivative method (ELD–MPPT). The explicit expressions for the response properties in each of these MPPT up to the quadratic response [μ, α(−ω₁, ω₁), β(−ω_σ, ω₁, ω₂)] at an arbitrary correlated order are given. Calculations of the dynamic polarizabilities and hyperpolarizabilities dependent on one frequency at the second‐order MPPT (MP2), in the QED method (QED–MP2) and in the ELD method (ELD–MP2), are examined for 10‐electron systems: hydrogen fluoride and neon. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 251–271, 1999     

Adaptation of one‐electron basis sets to spatial confinements

A method that generates out of a given orbital basis set its analog appropriate for describing the effects of a spatial confinement is presented. The method is based on the requirement that the one‐particle model spaces for the confined and for the unconfined systems are equivalent in the sense of a criterion derived from the basis‐set‐generating eigenvalue equations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 341–347, 1999