Laplacian eigenvalue distribution, diameter and domination number of trees

For a graph $G$ with domination number $\gamma$, Hedetniemi, Jacobs and Trevisan [European Journal of Combinatorics 53 (2016) 66-71] proved that $m_{G}[0,1)\leq \gamma$, where $m_{G}[0,1)$ means the number of Laplacian eigenvalues of $G$ in the interval $[0,1)$. Let $T$ be a tree with diameter $d$. In this paper, we show that $m_{T}[0,1)\geq (d+1)/3$. However, such a lower bound is false for general graphs. All trees achieving the lower bound are completely characterized. Moreover, for a tree $T$, we establish a relation between the Laplacian eigenvalues, the diameter and the domination number by showing that the domination number of $T$ is equal to $(d+1)/3$ if and only if it has exactly $(d+1)/3$ Laplacian eigenvalues less than one. As an application, it also provides a new type of trees, which show the sharpness of an inequality due to Hedetniemi, Jacobs and Trevisan

The Application of Dead Trees or Dying Trees in Landscape Design

In the development of landscape design, plants have always been one of the important elements in the landscape design, and play a very important role in the landscape. In the selection and application of landscape plants, living plants have always occupied a dominant position, but the research and application of dead trees are few. People tend to think that dead plants are no longer valuable, and all dead trees should be removed or replaced. In a sense, this is a waste of resources, and also increases the cost of landscape. In fact, the proper use of dead trees in landscapes design is more likely to display the artistic conception and theme of the landscape. In many natural landscapes, large trees, ancient trees and precious tree die because of natural laws or natural disasters, forming withered trees. This kind of withered tree endows the site with certain historical connotation, which could narrate the history and ecological change of site to people and evoke the imagination of people to the past. In addition, these dead wood still have high economic, ornamental, ecological and cultural values.This study focused on dead trees and dying trees as its subject, analyzing the outstanding dead trees application cases in natural landscape, and discusses the different functions of dead tree, such as ecological function, ornamental function, cultural function and others. In addition, the Beijing Wild Duck Lake National Wetland Park will serve as a special experimental site, dead tree will be designed and applied in the lake of park. And based on these data analyses, the final chapter will return to address the research questions and offer advice on how to apply dead tree to urban landscape and further enhance the value of dead trees in landscape design

Facile synthesis of chitosan-capped ZnS quantum dots as an eco-friendly fluorescence sensor for rapid determination of bisphenol A in water and plastic samples

This paper describes a novel eco-friendly fluorescence sensor for determination of bisphenol A (BPA) based on chitosan-capped ZnS quantum dots (QDs). By using safe and inexpensive materials, nontoxic ZnS QDs were synthesized via an environment-friendly method using chitosan as a capping agent. The as-prepared ZnS QDs exhibited characteristic absorption (absorbance edge at 310 nm) and emission (maxima at 430 nm) spectra with a relatively high fluorescence quantum yield of 11.8%. Quantitative detection of BPA was developed based on fluorescence quenching of chitosan-capped ZnS QDs with high sensitivity and selectivity. Under optimal conditions, the fluorescence response of ZnS QDs was linearly proportional to BPA concentration over a wide range from 0.50 to 300 mu g L-1 with a detection limit of 0.08 mu g L-1. Most of the potentially coexisting substances did not interfere with the BPA-induced quenching effect. The proposed analytical method for BPA was successfully applied to water and plastic real samples. The possible quenching mechanism is also discussed

Asymptotic in a class of network models with an increasing sub-Gamma degree sequence

For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.Comment: arXiv admin note: text overlap with arXiv:2002.12733 by other author

SEA: A Combined Model for Heat Demand Prediction

Heat demand prediction is a prominent research topic in the area of intelligent energy networks. It has been well recognized that periodicity is one of the important characteristics of heat demand. Seasonal-trend decomposition based on LOESS (STL) algorithm can analyze the periodicity of a heat demand series, and decompose the series into seasonal and trend components. Then, predicting the seasonal and trend components respectively, and combining their predictions together as the heat demand prediction is a possible way to predict heat demand. In this paper, STL-ENN-ARIMA (SEA), a combined model, was proposed based on the combination of the Elman neural network (ENN) and the autoregressive integrated moving average (ARIMA) model, which are commonly applied to heat demand prediction. ENN and ARIMA are used to predict seasonal and trend components, respectively. Experimental results demonstrate that the proposed SEA model has a promising performance

Influence of inductance variation on performance of a permanent magnet claw pole soft magnetic composite motor

Winding inductance is an important parameter in determining the performance of electrical machines, particularly those with large inductance variation. This paper investigates the influence of winding inductance variation on the performance of a three-phase three-stack claw pole permanent magnet motor with soft magnetic composite (SMC) stator by using an improved phase variable model. The winding inductances of the machine are computed by using a modified incremental energy method, based on three-dimensional nonlinear time-stepping magnetic field finite element analyses. The inductance computation and performance simulation are verified by the experimental results of an SMC claw pole motor prototype