Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

The Complete Proof of the Virial Theorem in the Refined TFD Theory for all Electrons of an Atom in a Solid

The complete proof of the virial theorem in refined Thomas-Fermi-Dirac theory for all electrons of an atom in a solid is given.

A Simplified Evaluation Procedure of the Scale of Fluctuation Combined Recurrence Averaging and Weighted Linear Regression

The divergence of properties from one location to another within a soil mass is termed spatial variability, which traditionally includes three parameters the mean, the standard deviation, and the scale of fluctuation, in order to stochastically describe a soil property. Among them, determining the scale of fluctuation in the evaluation of spatial variability of soil profiles is not easy due to soil condition complexity. A simplified procedure is presented in the paper to determine the scale of fluctuation combined recurrence averaging and weighted linear regression. The alternative approach utilizes widely usable spreadsheet to solve the problem more directly and efficiently.

The mean value concept in mono-linear regression of multi-variables and its application to trace studies in geosciences

IEECAS SKLLQG

CO2 Flux Estimation by Different Regression Methods from an Alpine Meadow on the Qinghai-Tibetan Plateau

National Key Research and Development Program [2010CB833500]; National Natural Science Foundation of China [30590381]; Chinese Academy of Sciences [KZCX2-YW-432]

Semisupervised Dimensionality Reduction and Classification Through Virtual Label Regression

Semisupervised dimensionality reduction has been attracting much attention as it not only utilizes both labeled and unlabeled data simultaneously, but also works well in the situation of out-of-sample. This paper proposes an effective approach of semisupervised dimensionality reduction through label propagation and label regression. Different from previous efforts, the new approach propagates the label information from labeled to unlabeled data with a well-designed mechanism of random walks, in which outliers are effectively detected and the obtained virtual labels of unlabeled data can be well encoded in a weighted regression model. These virtual labels are thereafter regressed with a linear model to calculate the projection matrix for dimensionality reduction. By this means, when the manifold or the clustering assumption of data is satisfied, the labels of labeled data can be correctly propagated to the unlabeled data; and thus, the proposed approach utilizes the labeled and the unlabeled data more effectively than previous work. Experimental results are carried out upon several databases, and the advantage of the new approach is well demonstrated.

Radiation effects on the immiscible polymer blend of nylon1010 and high-impact polystyrene (HIPS) I: Gel/dose curves, mathematical expectation theorem and thermal behaviour

This paper studies the radiation properties of the immiscible blend of nylon1010 and HIPS. The gel fraction increased with increasing radiation dose. The network was found mostly in nylon1010, the networks were also found in both nylon1010 and HIPS when the dose reaches 0.85 MGy or more. We used the Charleby-Pinner equation and the modified Zhang-Sun-Qian equation to simulate the relationship with the dose and the sol fraction. The latter equation fits well with these polymer blends and the relationship used by it showed better linearity than the one by the Charleby-Pinner equation. We also studied the conditions of formation of the network by the mathematical expectation theorem for the binary system. Thermal properties of polymer blend were observed by DSC curves. The crystallization temperature decreases with increasing dose because the cross-linking reaction inhibited the crystallization procession and destroyed the crystals. The melting temperature also reduced with increasing radiation dose. The dual melting peak gradually shifted to single peak and the high melting peak disappeared at high radiation dose. However, the radiation-induced crystallization was observed by the heat of fusion increasing at low radiation dose. On the other hand, the crystal will be damaged by radiation. A similar conclusion may be drawn by the DSC traces when the polymer blends were crystallized. When the radiation dose increases, the heat of fusion reduces dramatically and so does the heat of crystallization. (C) 1999 Elsevier Science Ltd. All rights reserved.

Selection for variables in quantitative structure-activity/property relationship studies - Comparison between methods of orthogonal descriptors and leaps-and-bounds regression analysis

In this paper, the comparison of orthogonal descriptors and Leaps-and-Bounds regression analysis is performed. The results obtained by using orthogonal descriptors are better than that obtained by using Leaps-and-Bounds regression for the data set of nitrobenzenes used in this study. Leaps-and-Bounds regression can be used effectively for selection of variables in quantitative structure-activity/property relationship(QSAR/QSPR) studies. Consequently, orthogonalisation of descriptors is also a good method for variable selection for studies on QSAR/QSPR.