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无限维欧氏空间的子空间的正交补

太原师范学院学报（自然科学版） 2009年第4期8卷 24-26页

作者：刘耀军张姗梅太原师范学院计算机科学与技术系太原师范学院数学系山西太原030012

文章利用标准正交基,证明了无限维欧氏空间的有限维子空间都有唯一的正交补.并进一步证明若无限维欧氏空间的有限维子空间是某正交变换的不变子空间,则其正交补也是该正交变换的不变子空间,但对无限维子空间结论不成立.

关键词：无限维欧氏空间正交补标准正交基子空间

Towards cultivar-oriented gene discovery for better crops

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The Crop Journal 2024年第3期12卷 670-675页

作者： Dengcai liu Triticeae Research Institute Sichuan Agricultural UniversityChengdu 611130SichuanChina

The continued expansion of the world population,increasingly inconsistent climate and shrinking agricultural resources present major challenges to crop ***,the increasing ability to discover and manipulate genes creates new opportunities to develop more productive and resilient *** genes have been described in papers as being beneficial for yield ***,few of them have been translated into increased yield on *** contrast,commercial breeders are facing gene decidophobia,i.e.,puzzled about which gene to choose for breeding among the many identified,a huge chasm between gene discovery and cultivar *** purpose of this paper is to draw attention to the shortfalls in current gene discovery research and to emphasise the need to align with cultivar *** methodology dictates that genetic studies not only focus on gene discovery but also pay good attention to the genetic backgrounds,experimental validation in relevant environments,appropriate crop management,and data *** close of the gaps should accelerate the application of molecular study in breeding and contribute to future global food security.

关键词： Cultivar innovation Data reusability Gene discovery Gene decidophobia Omnigenic model

Thermoregulatory molecular sieving in crystals

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Science China Materials 2024年第10期67卷 3419-3420页

作者： Guozhen liu Wanqin Jin Gongping liu State Key Laboratory of Materials-Oriented Chemical Engineering College of Chemical EngineeringNanjing Tech UniversityNanjing 211800China

Sub-nanometer channels for the selective recognition of the components in chemical mixtures from others play a crucial role in the adsorption and membrane separation[1].It remains a grand challenge to separate small m... 详细信息

关键词： structure. molecular separation

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例外代数G_2的实现

山西矿业学院学报 1995年第3期13卷 298-300页

作者：刘耀军山西大学师范学院

寻找李代数的最简单的实现是结构理论中十分有益的工作,本文将借助Kac-Moody代数给出G_2型单李代数的一个十分简单的实现。

关键词：代数实现例外代数

Breakdown of effective medium theory:A study of photonic spin Hall effect in deep-subwavelength all-dielectric multilayers

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Science China(Physics,Mechanics & Astronomy) 2024年第4期67卷 173-174页

作者： Yongmin liu Department of Mechanical and Industrial Engineering Northeastern UniversityBoston 02115USA Department of Electrical and Computer Engineering Northeastern UniversityBoston 02115USA

Effective medium theory(EMT)has been widely applied in material science,electromagnetics and photonics to determine the effective material properties for inhomogeneous composites comprising subwavelength *** versatility of this foundational approach has been established through its application in classical Maxwell-Garnet models,which encompass relatively simple structures。

关键词： composites theory dielectric

Fatigue-resistant sliding ferroelectricity

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Science China Materials 2024年第10期67卷 3417-3418页

作者： Zheng liu School of Materials Science and Engineering Nanyang Technological UniversitySingapore 639798Singapore

The direction of spontaneous polarization in ferroelectricity can be reoriented by an external electric *** special feature of ferroelectricity is important candidates for fabricating advanced nonvolatile random-access memory[1].However,repeatedly switching polarization induces the ferroelectric device performance degenerates due to a reduction of polarization.

关键词： polarization ferroelectric field.

A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

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Acta Mathematica Scientia 2024年第4期44卷 1337-1346页

作者： Xiaosong liu Taishun liu School of Mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048China Department of Mathematics Huzhou UniversityHuzhou 313000China

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of *** next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of *** results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

关键词： refined Schwarz-Pick estimate bounded holomorphic mapping Carathéodory metric first order Fréchet derivative higher order Fréchet derivatives

The important role of Turbidity Maximum Zone in sedimentary dynamic of estuarine mangrove swamp

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Frontiers of Earth Science 2024年第1期18卷 219-226页

作者： Tao liu Ying liu Baoqing HU Key laboratory of Environment Change and Resources Use in Beibu Gulf(Ministry of Education) Nanning Normal UniversityNanning 530001China School of Civil Engineering and Architecture Guangxi UniversityNanning 530004China

Sedimentation is a key process affecting wetland sustainability and carbon burial *** context of sea level rise,climate change and human activities,further understanding about the sedimentary dynamic in wetland is critical in predicting the landscape evolution or the change in carbon burial *** this study,based on the field hydrological observation in a mangrove system in the Nanliu River estuary,we found the net flux of suspended sediment to mangrove is 39−72 kg/m in tidal cycles with Turbidity Maximum Zone(TMZ)forming in surface layer and only is 9−18 kg/m in tidal cycles without *** higher net flux of suspended sediment to mangrove in tidal cycles with TMZ forming in surface layer is attributed to high SSC in rising tide and intense flocculation in *** significant discrepancy in sedimentation rate in the mangrove patches also can be explained by the probability of TMZ forming in the surface layer of *** future,rapid sea level rising may lead to the change of TMZ pattern in estuary,which will result in non-negligible variation in sedimentation rate in *** to the present data of sedimentation rate in wetlands,the fragility of wetlands in river estuary may be miscalculated.

关键词： mangrove wetland sedimentation Turbidity Maximum Zone Nanliu River

Compact multilayer liquid crystal polymer lowpass filter with 8-shaped inductor

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The Journal of China Universities of Posts and Telecommunications 2024年第3期31卷 80-86页

作者： liu Weihong Wang Guoxiu liu Qingran School of Electronic Engineering Xi'an University of Posts and TelecommunicationsXi'an 710121China

Lumped element lowpass filter(LPF)for ultra-high frequency(UHF)radio frequency(RF)front-end system is presented based on multilayer liquid crystal polymer(LCP).The lumped element LPF can achieve miniaturization and one transmission zero on the stopband by the 8-shaped *** lumped element LPF is fabricated on a 4-layer LCP substrate with a compact size of 9 mm×14 mm×0.193 *** measured cut off frequency of the lumped element LPF is 0.5 GHz with insertion loss(IL)less than 0.37 *** measured and simulated results suggest that it is a possible candidate for the application of UHF RF front-end system.

关键词： lowpass filter(LPF) multilayer liquid crystal polymer(LCP) miniaturization 8-shaped inductor