The Extremal Function for Two Disjoint Cycles *

Abstract A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order n ≥ 9 and size at least 7n−13 2 contains two disjoint theta graphs. We also show that every 2-edge-connected graph of order n ≥ 6 and size at least 3n − 5 contains two disjoint cycles, such that any specified vertex with degree at least three belongs to one of them. The lower bound on size in both are sharp in general

The Analysis of Consumer Behavior of Fresh- products E-Business—Based on Research in Chengdu

Experts were not optimistic about the sale of fresh products on internet a few years ago,because their prices are low while logistic costs are high. But according to the statistics in recent 2 years, the growth rate of sales of the fresh products on internet is amazing. After making an investigation of consumer behavior of fresh products E-business platforms in Chengdu city, the authors analyze the consumers’ behavior of fresh-products E-business and find the key factors affecting their purchase behavior via internet

Multi-product firms, product quality heterogeneity and trade liberalization

This paper develops a model of multi-product firms with endogenous quality across products within a firm. The model can reconcile the empirical fact that product quality and market size exhibit an inverted U relationship. In our model, on the one hand a larger market has a larger scope of quality differentiation and induces firms to increase quality; on the other hand, market competition is more intense in a larger market, exerting a negative influence on quality. We show that the model without taking quality differentiation into consideration could significantly underestimate the market competition and welfare. Moreover, our numerical analysis suggests that the model without taking quality differentiation into consideration could also significantly overestimate the gains of trade liberalization

Quantitative investment decisions based on machine learning and investor attention analysis

According to the trading rules and financial data structure of the stock index futures market, and considering the impact of major emergencies, we intend to build a quantitative investment decision-making model based on machine learning. We first adopt the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) signal decomposition technology to separate the short-term noise, cycle transformation and long-term trend from the original series, and use the CSI 500 Baidu index series to reflect the investors’ attention, which provides data support for establishing a more effective forecasting model. Then, the CEEMDANBP neural network model is designed based on the obtained effective information of low-frequency trend series, investor attention index and CSI 500 stock index futures market transaction data. Finally, an Attention-based Dual Thrust quantitative trading strategy is proposed and optimized. The optimized Attention-based Dual Thrust strategy solves the core problem of breakout interval determination, effectively avoids the risk of subjective selection, and can meet investors’ different risk preferences. The quantitative investment decision-making model based on CEEMDAN-BP neural network utilizes the advantages of different algorithms, avoids some defects of a single algorithm, and can make corresponding adjustments according to changes in investors’ attention and the occurrence of emergencies. The results show that considering investor attention can not only improve the predictive ability of the model, but also reduce the cognitive bias of the market, effectively control risks and obtain higher returns. First published online 24 August 202

FDI deregulation and firm innovation: Evidence from firm patents

This paper studies whether inward FDI deregulation promotes innovation by firms in the host country. A theoretical framework, in which the entry of additional foreign firms is associated with both spillover and competition effects, is built to guide the empirical evaluation. Exploiting data on Chinese firm-level patents in a difference-in-differences setting, this paper finds a positive and significant impact of FDI deregulation on firm innovation. Moreover, we find that FDI deregulation had a heterogeneous effect on firms: the impact was prominent on firms with high productivity while being insignificant on firms with low productivity.</p

Wavelength-Flexible Thulium-Doped Fiber Laser Based on Digital Micromirror Array

Wavelength-tunable thulium-doped fiber laser is demonstrated employing a digital micromirror device (DMD) in combination with a fixed grating. The diffraction property of four typical models of DMDs and its steering efficiency for the laser system are analyzed based on two-dimensional grating theory. By spatially modulating reflective patterns on a DMD, the stable, fast, and flexible tuning of lasing wavelength from 1930 nm to 2000 nm is achieved with wavelength tuning accuracy of 0.1 nm. The side-mode suppression ratio is larger than 50 dB around the 2 &mu;m band with 3 dB linewidth less than 0.05 nm. The wavelength drift and power fluctuation are lower than 0.05 nm and 0.1 dB within 1 h at the room temperature, respectively

Programmable Spectral Filter in C-Band Based on Digital Micromirror Device

Optical filters have been adopted in many applications such as reconfigurable telecommunication switches, tunable lasers and spectral imaging. However, most of commercialized filters based on a micro-electrical-mechanical system (MEMS) only provide a minimum bandwidth of 25 GHz in telecom so far. In this work, the programmable filter based on a digital micromirror device (DMD) experimentally demonstrated a minimum bandwidth of 12.5 GHz in C-band that matched the grid width of the International Telecommunication Union (ITU) G.694.1 standard. It was capable of filtering multiple wavebands simultaneously and flexibly by remotely uploading binary holograms onto the DMD. The number of channels and the center wavelength could be adjusted independently, as well as the channel bandwidth and the output power. The center wavelength tuning resolution of this filter achieved 0.033 nm and the insertion loss was about 10 dB across the entire C-band. Since the DMD had a high power handling capability (25 KW/cm2) of around 200 times that of the liquid crystal on silicon (LCoS) chip, the DMD-based filters are expected to be applied in high power situations