On sign-changing solutions for nonlinear operator equations

AbstractIn this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett–Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638–654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations

Eigenmodes of a reflective twisted-nematic liquid-crystal cell

The eigenmodes of a reflective twisted-nematic liquid-crystal (TN LC) cell are analyzed based on the Jones matrix method. Two models are developed to describe the LC system in the low- and high-voltage regimes. The simulated transmission spectra of LC Fabry-Perot etalons are used to investigate the eigenmodes. In a general reflective TN LC cell, the eigenmodes are two orthogonal linear polarization states. Under some specific conditions, these two linear polarization states will approach the bisector or orthogonal to the bisector of the TN LC cell. This bisector effect is useful for reducing the operating voltage and enhancing the contrast ratio of LC display devices and for eliminating the mode coupling of the tunable Fabry-Perot etalons

A series of nano/micro-sized metal-organic frameworks with tunable photoluminescence properties

Present studies on metal-organic frameworks (MOF) mainly focus on macro-scaled single crystals. However, the realization of MOF nanocrystals via a bottom-up one-step method still remains a significant challenge. Here, hierarchically assembled nanostructures of lanthanide-based MOFs with 1D and 3D morphologies have been successfully fabricated via a simple and rapid solution phase method at room temperature. Upon UV excitation, these nanomaterials exhibit highly efficient tunable luminescence properties, which come from the Eu3+ or Tb3+ ions. Moreover, white-light emission can be achieved by co-activating the organic ligand, Eu3+ and Tb3+ ions in the nano-MOFs. This journal i

Effects of tea garden soil on aroma components and related gene expression in tea leaves

In order to explore the effect of soil on the synthesis of aroma components in tea leaves, tea seedlings replanted in tea rhizosphere soil of different ages were used as research materials. Tea seedlings were replanted in soils aged 0, 4, 9, and 30 years, and after one year of growth, 34, 37, 29, and 26 substances were detected in the tea leaves, respectively, using gas chromatography-mass spectrometry (GC-MS). The relative contents of terpenoids and alcohols in the tea leaves dropped from 66.40% to 44.52% and 5.21% to 2.61%, respectively, as the age of the rhizosphere soil increased. Aldehydes, esters, and nitrogen compounds increased from 3.80% to 22.36%, 1.33% to 12.02%, and 3.13% to 19.96%, respectively, as the age of the rhizosphere soil increased. Gene differential expression measured by fluorescence quantitative PCR (qRT-PCR) showed that the number of nerolidol synthetase and linalool synthase genes in tea leaves increased significantly, and the terpineol synthetase, phellandrene synthase, myrcene synthetase, ocimene synthase, limonene synthetase, germacrene synthase, and farnesene synthase genes declined significantly with the increase in soil age. In summary, as the number of years tea had been planted in the soil increased, the soil significantly affected the expression of terpene synthase genes in tea leaves, and then the composition and content of aroma substances in tea leaves changed. The results provide a theoretical basis for the improvement of tea quality

Integrating Overlapping Structures and Background Information of Words Significantly Improves Biological Sequence Comparison

Word-based models have achieved promising results in sequence comparison. However, as the important statistical properties of words in biological sequence, how to use the overlapping structures and background information of the words to improve sequence comparison is still a problem. This paper proposed a new statistical method that integrates the overlapping structures and the background information of the words in biological sequences. To assess the effectiveness of this integration for sequence comparison, two sets of evaluation experiments were taken to test the proposed model. The first one, performed via receiver operating curve analysis, is the application of proposed method in discrimination between functionally related regulatory sequences and unrelated sequences, intron and exon. The second experiment is to evaluate the performance of the proposed method with f-measure for clustering Hepatitis E virus genotypes. It was demonstrated that the proposed method integrating the overlapping structures and the background information of words significantly improves biological sequence comparison and outperforms the existing models

Direction controllable linearly polarized laser from a dye-doped cholesteric liquid crystal

We demonstrate a direction controllable linearly polarized laser from a dye-doped cholesteric liquid crystal (CLC) in a homogeneous cell coated with a metallic mirror on the inner side of a glass substrate. Due to coherent superposition of two orthogonal polarization states, the output laser light becomes linearly polarized and its output energy is greatly enhanced. Moreover, the linear polarization direction angle is proportional to the product of the CLC effective birefringence and cell gap. Hence direction tunable laser devices can be demonstrated by controlling the cell gap and the operating temperature

Identification of microRNAs Involved in the Host Response to Enterovirus 71 Infection by a Deep Sequencing Approach

Role of microRNA (miRNA) has been highlighted in pathogen-host interactions recently. To identify cellular miRNAs involved in the host response to enterovirus 71 (EV71) infection, we performed a comprehensive miRNA profiling in EV71-infected Hep2 cells through deep sequencing. 64 miRNAs were found whose expression levels changed for more than 2-fold in response to EV71 infection. Gene ontology analysis revealed that many of these mRNAs play roles in neurological process, immune response, and cell death pathways, which are known to be associated with the extreme virulence of EV71. To our knowledge, this is the first study on host miRNAs expression alteration response to EV71 infection. Our findings supported the hypothesis that certain miRNAs might be essential in the host-pathogen interactions

S3E: A Large-scale Multimodal Dataset for Collaborative SLAM

With the advanced request to employ a team of robots to perform a task collaboratively, the research community has become increasingly interested in collaborative simultaneous localization and mapping. Unfortunately, existing datasets are limited in the scale and variation of the collaborative trajectories, even though generalization between inter-trajectories among different agents is crucial to the overall viability of collaborative tasks. To help align the research community's contributions with realistic multiagent ordinated SLAM problems, we propose S3E, a large-scale multimodal dataset captured by a fleet of unmanned ground vehicles along four designed collaborative trajectory paradigms. S3E consists of 7 outdoor and 5 indoor sequences that each exceed 200 seconds, consisting of well temporal synchronized and spatial calibrated high-frequency IMU, high-quality stereo camera, and 360 degree LiDAR data. Crucially, our effort exceeds previous attempts regarding dataset size, scene variability, and complexity. It has 4x as much average recording time as the pioneering EuRoC dataset. We also provide careful dataset analysis as well as baselines for collaborative SLAM and single counterparts. Data and more up-to-date details are found at https://github.com/PengYu-Team/S3E