On the spectral radius of weighted trees with given number of pendant vertices and a positive weight set

Let 𝒯(n,?r;?W _n?1) be the set of all n-vertex weighted trees with r vertices of degree 2 and fixed positive weight set W _n?1, 𝒫(n,?γ;?W _n?1) the set of all n-vertex weighted trees with q pendants and fixed positive weight set W _n?1, where W _n?1?=?{w ₁,?w ₂,?…?,?w _n?1} with w ₁???w ₂???···???w _n?1?>?0. In this article, we first identify the unique weighted tree in 𝒯(n,?r;?W _n?1) with the largest adjacency spectral radius. Then we characterize the unique weighted trees with the largest adjacency spectral radius in 𝒫(n,?γ;?W _n?1).     

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.     

Consistency analysis of the spectrum and prosody within a syllable for Mandarin speech

This work presents a study of Mandarin speech focusing on consistency analysis of the spectrum and prosody within syllables. Identified as a result of inspection of the human pronunciation process, this consistency can be interpreted as a high correlation between the warping curves of the spectrum and the prosody intra a syllable. The consistency analysis consisted of three steps. First, the hidden Markov model algorithm was used to decode the hidden Markov model‐state sequences within a syllable, while at the same time dividing them into three segments. Second, based on a designated syllable, the vector quantization (VQ) with the Linde–Buzo–Gray algorithm was employed to train the VQ codebooks of the prosodic vector of each segment. Third, the prosodic vector of each segment was encoded as an index using the VQ codebooks, and then, to analyze the consistency, the probability of each possible path was evaluated as a prerequisite. Finally, two syllables were used as examples to verify the consistency property found in the experiments. It is demonstrated experimentally that there is definitely consistency in the case where the syllable is located in exactly the same word. These results offer a research direction in that the warping process between the spectrum and the prosody intra a syllable must be considered in text‐to‐speech systems to improve the synthesized speech quality. Copyright © 2013 John Wiley & Sons, Ltd.     

iVI-TD-DFT: An iterative vector interaction method for exterior/interior roots of TD-DFT

The recently proposed iterative vector interaction (iVI) method for large Hermitian eigenvalue problems (Huang et al., J. Comput. Chem. 2017, 38, 2481) is extended to generalized eigenvalue problems, HC = SCE , with the metric S being either positive definite or not. Although, it works with a fixed-dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The algorithms are further specialized to nonrelativistic and relativistic time-dependent density functional theories (TD-DFT) by taking the orbital Hessian as the metric (i.e., the inverse TD-DFT eigenvalue problem) and incorporating explicitly the paired structure into the trial vectors. The efficacy of iVI-TD-DFT is demonstrated by various examples. © 2018 Wiley Periodicals, Inc.     

Conversion issues between microwave radiance and brightness temperature

Microwave radiances are usually converted into brightness temperatures for data assimilation and retrievals. The Rayleigh-Jeans approximation has been believed to be a good approximation for the conversion at low frequencies, but inaccurate at high frequencies. However, the simplified radiative transfer models under the Rayleigh-Jeans approximation (hereafter referred as BT-RTE) have been successfully applied in radiance simulations for frequencies below 183 GHz, which has somewhat puzzled the radiative transfer community. This paper clarifies the confusion. In addition, the conversion formula for the third and the fourth Stokes components are derived.Simulations for a polarized sensor, the Special Sensor Microwave Imager and Sounder, show that the BT-RTE is generally accurate. Results for a polarimetric sensor, WINDSAT, show that the third and the fourth Stokes radiances should be converted using the exact conversion formula given in this study rather than using a direct Planck function conversion.     

Topological Structure of Entropy of 4-Dimensional Axisymmetric Black Holes

Using the relationship between the entropy and the Euler characteristic, an entropy density is introduced to describe the inner topological structure of the entropy of 4-dimensional axisymmetric black holes. It is pointed out that the density of entropy is determined by the singularities of the timelike Killing vector field of spacetime, and these singularities carry the topological numbers, Hopf indices and Brouwer degrees, which are topological invariants. At last, Kerr–Newman black hole as an example of axisymmetric black holes is given. What’s more, the entropy and the latent heat of the topological phase transition of the black hole mentioned above are calculated and the latent heat just lies in the range of the energy of gamma ray bursts. This work is supported in part by the NSFs of China under Grant No. 10575068 and of Shanghai Municipal Committee of Science and Technology under Grant No. 04ZR14059 and Shanghai Leading Academic Discipline Project under Project Number: T0104.     

Effects of third-order dispersion on soliton switching in fiber nonlinear directional couplers

The split-step Fourier method is used to study the energy switching characteristics of fiber nonlinear directional couplers with the third-order dispersion. The effects of the third-order dispersion increases with the third-order dispersion coefficient and input power and result in pulse shift and energy decreases. Adding high-order nonlinear can partly overcomes these effects.     

Soliton Propagation in Birefringent Fibers

In this article, the propagation of solitons in a single mode fiber with polarization mode dispersion (PMD) is analyzed. In optical fibers, the randomly varying birefringence degrades soliton transmission system in two aspects. First, the dispersive waves cause pulse broadening. Second, the dispersive waves interact with other soliton pulses. Here we studied the effects of PMD on a single pulse and the variation of pulse broadening, energy decay, and degree of polarization on a single soliton pulse propagating over a very long distance.