“‘关·联’数学”的教学主张与实施策略

“‘关·联’数学”主张以学生个体素养提升为目标,从整体的视角解读文本,抓住数学本质,关注知识的发生过程和学生的认知过程,促进学生的思维发展。在“‘关•联’数学”课堂教学中,教师应注意找准关点,确立联动目标;明晰关子,连接新旧认知;辨析关系,联系数学思想;融通关节,促进联想生成。

Adaptive topology learning of camera network across non-overlapping views

An adaptive topology learning approach is proposed to learn the topology of a practical camera network in an unsupervised way. The nodes are modeled by the Gaussian mixture model. The connectivity between nodes is judged by their cross-correlation function, which is also used to calculate their transition time distribution. The mutual information of the connected node pair is employed for transition probability calculation. A false link eliminating approach is proposed, along with a topology updating strategy to improve the learned topology. A real monitoring system with five disjoint cameras is built for experiments. Comparative results with traditional methods show that the proposed method is more accurate in topology learning and is more robust to environmental changes.

Degradation Process of Coated Tinplate by Phase Space Reconstruction Theory

The degradation process of organosol coated tinplate in beverage was investigated by electrochemical noise (EN) technique combined with morphology characterization.EN data were analyzed using phase space reconstruction theory.With the correlation dimensions obtained from the phase space reconstruction,the chaotic behavior of EN was quantitatively evaluated.The results show that both electrochemical potential noise (EPN) and electrochemical current noise (ECN) have chaotic properties.The correlation dimensions of EPN increase with corrosion extent,while those of ECN seem nearly unchanged.The increased correlation dimensions of EPN during the degradation process are associated with the increased susceptibility to local corrosion.

A New Model for Prediction of Mean Liquid Circulating Velocity in Bubble Columns

A new model without any fitting parameter for estimating the mean liquid recirculating velocity has been derived from previous work directly. The prediction agrees with experimental data reasonably well. Accurency of prediction from the new model is comparable with the models reported in the literature. However, the new model has a potential capability to predict the average liquid recirculation velocity at elevated pressure bubble columns since n and c is developed under pressure. However this needs to be further tested experimentally.

Path Integral Liouville Dynamics Simulations of Vibrational Spectra of Formaldehyde and Hydrogen Peroxide

Formaldehyde and hydrogen peroxide are two important realistic molecules in atmospheric chemistry.We implement path integral Liouville dynamics(PILD)to calculate the dipolederivative autocorrelation function for obtaining the infrared spectrum.In comparison to exact vibrational frequencies,PILD faithfully captures most nuclear quantum effects in vibrational dynamics as temperature changes and as the isotopic substitution occurs.

An intuitive general rank-based correlation coefficient

Correlation analysis is an effective mechanism for studying patterns in data and making predictions.Many interesting discoveries have been made by formulating correlations in seemingly unrelated data. We propose an algorithm to quantify the theory of correlations and to give an intuitive, more accurate correlation coefficient.We propose a predictive metric to calculate correlations between paired values, known as the general rank-based correlation coefficient. It fulfills the five basic criteria of a predictive metric： independence from sample size,value between-1 and 1, measuring the degree of monotonicity, insensitivity to outliers, and intuitive demonstration.Furthermore, the metric has been validated by performing experiments using a real-time dataset and random number simulations. Mathematical derivations of the proposed equations have also been provided. We have compared it to Spearman＇s rank correlation coefficient. The comparison results show that the proposed metric fares better than the existing metric on all the predictive metric criteria.

Comultiplications on a wedge of two spheres

In this paper we study the set of comultiplications on a wedge of two spheres. We are primarily interested in the size of this set and properties of the comultiplications such as associativity and commutativity. Our methods involve Whitehead products in wedges of spheres and the Hopf-Hilton invariants. We apply our results to specific examples and determine the number of comultiplications, associative comultiplications and commutative comultiplications in these cases.

Correlation functions of gauged linear σ-model

This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve.

Smith normal forms of incidence matrices

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current understanding are indicated.

Effect of Transverse Correlation Function on the Thermodynamic Quantities of Ferromagnetic Systems

The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the short-range interaction between spins, so that lowers the internal energy and consequently raises the free energy. It also means the introduction o[ some ordering, and hence lowers the entropy. It is depressed by the field which forces the spins to turn to the field direction, so that it decreases with the field when temperature is fixed. The low-temperature expansion of the energy shows that the inclusion of the transverse correlation at least partly considers the interaction between spin waves.

Measuring Nonlinear Dependence Between Time Series Based on Correlation Dimension

In this paper, it is proved that the correlation dimension estimate of a nonlinear dynamical system with its multivariate observation series is the same as that with its univariate observation series. Based on this result, an inference method is presented, and the Nonlinear Dependence Coefficient is defined. This method is designed for testing nonlinear dependence between time series, and can be used in economic analysis and forecasting. Numerical results show the method is effective.