基于单体的Q和e值绘制二元共聚双曲线*

采用Matlab中的Plot函数,首次以单体的Q、e值为中间变量,绘制出二元共聚双曲线。将二元共聚物组成曲线F1-f1和F2-f2同时呈现在一个图上,使隐含的第二单体的共聚行为可视化,有助于加深学习者对二元共聚的理解。     

Rotational and rovibrational transitions in the a 1Δ2 and b 1Σ+0+ states of sulfur monoxide radical

ABSTRACT

Sulfur monoxide radical has widely been detected in outer space using ground-state spectroscopy. The a ¹Δ₂ and b ¹Σ⁺₀₊ states of this radical have low excitation energies, and they possibly exist in outer space. In this work, the potential energy curves and dipole moment functions of the two states were evaluated using the complete active space self- consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The transition line positions, oscillator strengths, band transition dipole matrix elements, Einstein A coefficients, and Franck–Condon factors of all transitions were calculated for lower vibrational levels at rotational angular momentum quantum number J up to 150. The transition line positions calculated in this study are in good agreement with the experimental results. The rovibrational transition became noticeably weak at Δυ > 5. Comparing the results of a ¹Δ₂ and b ¹Σ⁺₀₊ states reported in this paper with the previous values, we conclude that these results are the most accurate and complete to date.     

Tribology of thin wetting films between bubble and moving solid surface

This work shows a successful example of coupling of theory and experiment to study the tribology of bubble rubbing on solid surface. Such kind of investigation is reported for the first time in the literature. A theory about wetting film intercalated between bubble and moving solid surface was developed, thus deriving the non-linear evolution differential equation which accounted for the friction slip coefficient at the solid surface. The stationary 3D film thickness profile, which appears to be a solution of the differential equation, for each particular speed of motion of the solid surface was derived by means of special procedure and unique interferometric experimental setup. This allowed us to determine the 3D map of the lift pressure within the wetting film, the friction force per unit area and the friction coefficient of rubbing at different speeds of motion of the solid surface. Thus, we observed interesting tribological details about the rubbing of the bubble on the solid surface like for example:     

SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface

In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe₂O₄ composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices.     

Explicit maximal and minimal curves over finite fields of odd characteristics

In this work we present explicit classes of maximal and minimal Artin–Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].     

A density functional theory-time-dependent density functional theory investigation of photo-induced hydrogen bond and proton transfer for 2-(3,5-dichloro-2,6-dihydroxy-phenyl)-benzoxazole-6-carboxylicacid

Given the paramount importance of excited-state relaxation in the photochemical process, excited-state hydrogen bonding interactions and excited-state intramolecular proton transfer (ESIPT) are always hot topics. In this work, we theoretically explore the excited-state dynamical behaviors for a novel 2-(3,5-dichloro-2,6-dihydroxy-phenyl)-benzoxazole-6-carboxylicacid (DDPBC) system. As two intramolecular hydrogen bonds (O1 H2⋯N3 and O4 H5⋯O6) exist in the DDPBC structure, we first check if the double proton transfer form cannot be formed in the S1 state. Then, we explore the changes of geometrical parameters involved in hydrogen bonds, based on which we confirm that the dual intramolecular hydrogen bonds are strengthened on photo-excitation. The O1 H2⋯N3 hydrogen bond particularly plays a more important role in excited state. When it comes to the photo-induced excitation, we find charge transfer and electronic density redistribution around O1 H2 and N3 atom moieties. We verify the ESIPT tendency arising from the O1 H2⋯N3 hydrogen bond. In the analysis of the potential energy curves, along with O1 H2⋯N3 and O4 H5⋯O6, we demonstrate that the ESIPT reaction should occur along with O1 H2⋯N3 rather than O4 H5⋯O6. This work not only clarifies the specific ESIPT mechanism for DDPBC system but also paves the way for further novel applications based on DDPBC structure in the future.     

A complete set of addition laws for incomplete Edwards curves

Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P₁, P₂ produce the sum P₁+P₂.     

Iterative process for G-multi degree reduction of Bézier curves

In this paper, the issue of multi-degree reduction of Bézier curves with C¹ and G²-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.