Valence Bond Study of Dissociation Behavior and Spectroscopic Constants for the Ground States of LiF and NaF

Ab initio VB calculations were used to determine the accurate spectroscopic parameters of the ground states of LiF and NaF. A set of potential energy curves corresponding to the ground states including ionic and covalent interactions, pure ionic interaction and covalent interaction were generated using the VBSCF method. Curve crossing in the dissociation processes of LiF and NaF was discussed. The optimized VB wave functions suggest that LiF and NaF are of high ionicity, and their ionic weights are 86 2% and 94 6%, respectively. NaF has a higher ionicity. The main difference between atom F and ion F - and the effect of the proper description of this difference on dissociation energies were investigated.

A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence

It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent com- bination, Zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.

Novel method to detect Hopf bifurcation in a delayed fractional-order network model with bidirectional ring structure

In this paper,we formulate and study a fractional-order network model with four neurons,bidirectional ring structure and self-delay feedback.For the scenario of nonidentical neurons,we develop a new algebraic technique to deal with the characteristic equation with e-4st(T is the self-feedback delay)term and thus establish the easy-tocheck criteria to determine the Hopf bifurcation point of self-feedback delay by fixing communication delay in its stable interval.For the scenario of identical neurons,we apply the crossing curves method to the fractional functional equations and thus procure the Hopf bifurcation curve.The obtained results accommodate the fact that the model cannot preserve its stability behavior when the self-feedback delay crosses the Hopf bifurcation point in the positive direction.Finally,we deliberate on the correctness of our methodology through two demonstration examples.

A defect recognition model for cross-section profile of hot-rolled strip based on deep learning

The cross-section profile is a key signal for evaluating hot-rolled strip quality,and ignoring its defects can easily lead to a final failure.The characteristics of complex curve,significant irregular fluctuation and imperfect sample data make it a challenge of recognizing cross-section defects,and current industrial judgment methods rely excessively on human decision making.A novel stacked denoising autoencoders(SDAE)model optimized with support vector machine(SVM)theory was proposed for the recognition of cross-section defects.Firstly,interpolation filtering and principal component analysis were employed to linearly reduce the data dimensionality of the profile curve.Secondly,the deep learning algorithm SDAE was used layer by layer for greedy unsupervised feature learning,and its final layer of back-propagation neural network was replaced by SVM for supervised learning of the final features,and the final model SDAE_SVM was obtained by further optimizing the entire network parameters via error back-propagation.Finally,the curve mirroring and combination stitching methods were used as data augmentation for the training set,which dealt with the problem of sample imbalance in the original data set,and the accuracy of cross-section defect prediction was further improved.The approach was applied in a 1780-mm hot rolling line of a steel mill to achieve the automatic diagnosis and classification of defects in cross-section profile of hot-rolled strip,which helps to reduce flatness quality concerns in downstream processes.

BUCKLING LOADS AND EIGENFREQUENCIES OF A BRACED BEAM RESTING ON AN ELASTIC FOUNDATION

The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated. sented. The eigenvalues vary with the different The exact solutions for the eigenvalues are preparameters and are especially sensitive to the brace location. As the beam of a continuous system has infinite eigenvalues and these eigenvalues are influenced differently by a brace, the eigenvalues show rich variation patterns. Because these eigenvalues physically correspond to the structure buckling loads and natural frequencies, the study on the eigenvalues variation patterns can offer a design guidance of using a lateral brace of translation spring to strengthen the structure.