Geometrical bounding of data space and nonlinear classification of chemical data using MPGA algorithm

This paper develops a multi-parturition genetic algorithm (MPGA) to be used in geometrical bounding of the overlapped clusters in a data set for the classification of chemical data. Two new operators have been introduced to modify the conventional genetic algorithm, namely, multi-parturition and decimation and orientated creation to improve the linear classification results and diminish the computational time. To circumvent the difficulty commonly encountered in the treatment of linearly inseparable chemical data sets, the optimized linear classifier is further modified to provide a complementary nonlinear classifier. For this reason the space regions of the overlapped clusters have been bounded by erection of half-hyperellipsoids over the linearly misclassified patterns. The proposed MPGA was applied to classify a number of chemical and other data sets with a dimension from 4 to 14. Experimental results have indicated that the proposed MPGA could classify seriously overlapped data sets with an acceptable error rate.     

The Sharma-Tasso-Olver-Burgers equation: its conservation laws and kink solitons

The present paper deals with the Sharma–Tasso–Olver–Burgers equation (STOBE) and its conservation laws and kink solitons. More precisely, the formal Lagrangian, Lie symmetries, and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws. Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods. Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons. According to the authors’ knowledge, the outcomes of the current investigation are new and have been listed for the first time.     

全新设计蛋白质的折叠机制

蛋白质全新设计和折叠研究是从两个不同的方向来理解蛋白质序列-结构-功能关系这一结构生物学重要问题. 蛋白质全新设计取得的成功实例一定程度上检验了人们对蛋白质结构和相互作用理解的准确性, 但它们中多数所表现的不同于天然蛋白质的折叠动力学特征也表明, 要达到最终的功能化实现目标还面临着不少的挑战. 本文综述了蛋白质全新设计的发展过程及现状, 蛋白质折叠研究在实验、理论及模拟方面的研究进展, 以及全新设计蛋白质的折叠机制的研究现状. 阐述了深入了解全新设计蛋白质与天然蛋白质折叠机制的不同, 可以为进一步有效地合理化设计蛋白质提供有益的参考.     

A simple mathematical model for free vibration analysis of combined system consisting of framed tube,shear core,belt truss and outrigger system with geometrical discontinuities

Dynamic analysis of beam-like structure is significantly important in modeling real cases such as tall buildings, aircraft wings, spacecraft antennas and many other applications. This paper tries to determine the first natural frequency of tall buildings including framed tube, shear core, belt truss and outrigger system with multiple jumped discontinuities in the cross section of framed tube and shear core. In this regard, the entire length of the tall building is partitioned into uniform segments between each two successive discontinuity points. The effect of belt truss and outrigger system is modeled as a concentrated rotational spring applied at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilever bars with multiple jumped discontinuities in the cross section for the analysis of their free vibration. In this paper, the continuous approach was accepted and by using the Hamilton’s variational principle, the general form of governing equation for free vibration of tall building can be obtained. By applying the separation of variable method on time and space, the governing Partial Differential Equation (PDE) of motion is reduced to an Ordinary Differential Equation (ODE) with one variable coefficient while the other coefficients are constant based on the assumption that the transverse displacement is a harmonic vibration. To find exact solution of ODE, we must have exact distribution of EI(x), AG(x), N(x) and m(x) in the height of the structure. Some of these parameters such as EI(x), AG(x) and m(x), are constant throughout the height of each segment. These parameters can be expressed exactly by using of multi criteria function, while N(x) is variable in the height of each segment. Therefore, the ODE by using the method of variable separation and partitioned method can be expressed for each segment. We must apply the continuity conditions in conjunction with different segments for obtaining unique mode shape for mentioned system. Tall building characteristics matrix can be derived based on the boundary conditions and the continuity conditions applied at the partitioned points. This matrix is particularly used to find combined system first natural frequency and mode shape. Three numerical examples with different stepped discontinuities in their cross sections are studied to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure’s dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages which require less time.     

基于景气指数的我国工业经济周期性波动特征及本轮波动特点研究

通过多方面收集与我国工业部门经济运行相关的月度经济指标,利用时差相关分析等方法从中筛选出我国工业经济运行的先行、一致和滞后指标,并利用国际上先进的合成指数方法构建了我国工业部门的景气指数,根据其波动态势具体分析了我国工业经济的周期性波动特征,并结合主要经济指标的变动对我国工业部门的本轮景气波动特点进行了具体分析。结果表明2000年以来我国工业经济共经历了三次完整地景气循环,现正处于第四次循环的下降期。其中第一轮循环属于典型的长扩张型周期,并且呈现明显的非对称性周期特征,第二轮循环属于典型的震荡型周期,且收缩幅度和扩张幅度明显缩小,受金融危机影响第三轮景气循环的谷底较深,但随后我国工业景气呈现强劲上升态势,目前工业景气指数处于下降期.     

Statistics of Polymer Solutions from Scaling Concepts for Geometry and Relativistic Self-Diffusion in Liquids

Basic results on conformational statistics of polymer solutions are derived from recent scaling concepts for geometry and a relativistic picture for Brownian self-diffusion in liquid media. Any chain conformation is interpreted as a geometrical state affected by its end-to-end dimension, which here denotes the mean deviation between geodesic paths diffusing in the relativistic liquid phase. Statistical polymer length distributions solve an ondulatory equation in non-Euclidean manifolds for coil extension and shape. When length scale is vanishing, the size scaling is found again in terms of parallelism angle rotations. The characteristic chain ratio identifies instead an average metric coefficient, originating topologically from rotational degrees of freedom internal to single molecules.     

The incarnate rhythm of geometrical knowing

Rhythm is a fundamental dimension of human nature at both biological and social levels. However, existing research literature has not sufficiently investigated its role in mathematical cognition and behavior. The purpose of this article is to bring the concept of “incarnate rhythm” into current discourses in the field of mathematical learning and knowing. Our study is part of a 2-year longitudinal project focused on theorizing the role of the body in elementary students’ mathematics. Drawing on an exemplary episode in which a group of third-graders were asked to classify three-dimensional objects, we illustrate how rhythmical patterns can emerge in dimensions such as beat gestures, body position, and object orientation. Based on a detailed microanalysis of the episode, which was selected among other structurally similar examples, we conclude that incarnate rhythm is an irreducible feature in the emergence of mathematical sense and the production of mathematical communication.     

铅硫二元团簇Pb5S+4的理论研究

用密度泛函方法对铅硫二元团簇Ｐb５Ｓ４＋的结构和性能进行了理论研究。结果表明,具 有Ｃ,对称性的笼状结构的异构体最稳定。根据计算所推测的该团簇的性质与实验结果下一致。     

MSINDO study of water adsorption on NiO surfaces

The dissociation of water adsorbed on the surface of NiO was investigated by using the semi-empirical SCF MO method MSINDO. Simulations were based on embedded cluster models representing the (100) surface, with and without a monatomic step. The angle formed between the metal adsorption site and the O–H bond associated with water has been found to be critical to the energetics of the dissociation process. Based on this criterion, it was shown that water dissociation is favorable on the stepped surface, but highly unlikely on the planar surface. In addition, the activation energy required for water dissociation in a monatomic NiO step was considerably lower than for dissociation at the planar surface. The high activation energy associated with water dissociation on the planar surface is attributed to the rigidity of the NiO lattice. Dedicated to Prof. K. Jug in honor of his 65th birthday     

Properties of proton-rich nuclei in a three-body model

Using a three-body model and realistic two-body potentials, we investigate the properties of the nuclei ¹⁸Ne and ²⁸S near the proton dripline. We figure out the two-proton separation energies, occupation of the valence protons, root-mean-square radii of matter and the valence protons. Besides, the spatial correlation densities are displayed to reflect the correlation between the two valence protons. The first excited 0⁺ state of ¹⁸Ne is most likely to be a halo state according to our calculation. Turning off the Coulomb interactions among the three-body systems, we get the two-neutron separation energies and configuration of the valence neutrons of their corresponding mirror nuclei. The results indicate that the three-body model is proper to describe some proton-rich nuclei and can be used to deduce reliable information.