ESSENTIAL APPROXIMATE POINT SPECTRA FOR UPPER TRIANGULAR MATRIX OF LINEAR RELATIONS

When A E ∈LR（H） and B E ∈LR（K） are given, for C E∈LR（K, H） we denoteby Mc the linear relation acting on the infinite dimensional separable Hilbert space H Kof the formIn this paper, we give the necessary and sufficient conditionson A and B for wh{ch Mc is upper semi-Fredholm with negative index or Weyl for some C C ∈LR（K, H）.

Dynamic Response Analysis of Bird Strike on Aircraft Windshield Based on Damage-modified Nonlinear Viscoelastic Constitutive Relation

Damage-modified nonlinear viscoelastic constitutive equation and failure criterion are introduced and the three-dimensional incremental forms are deduced based on the updated Lagrangian approach. A simple tensile test model and a split Hopkinson pressure bar model are built to verify the accuracy of the subroutine implemented within the non-linear finite element program LS-DYNA. A numerical model of bird strike on windshield is established to study the responses of windshield under three different bird velocities at three sites. The bird is represented by a cylinder with a hemisphere at each end and the contact-impact coupling algorithm is used in this study. It is found that the implemented subroutine can properly describe the mechanical behavior of polymethyl methaerylate under low and high strain rates and large deformation, and can be used validly.

Application of Linear Thermodynamics to the Atmospheric System.Part Ⅱ: Exemplification of Linear Phenomenological Relations in the Atmospheric System

The linear phenomenological relations in the atmospheric boundary layer are proved indirectly using observational facts to combine linear thermodynamic theory and similarity theory in the boundary layer. Furthermore, it is proved that Ihe turbulent transport coefficients are in proportion to Ihe corresponding linear phenomenological coefficients. But the experimental facts show that the linear phenomenological relations are not (tenable in the atmospheric mixing layer because the turbulenl transport process is an intense non-linear process in the mixing layer. Hence the convection boundary layer is a thermodynamic stale in a non-linear region far from the equilibrium state. The geostrophic wind is a special cross-coupling phenomenon between the dynamic process and the thermodynamic process in the atmospheric system. It is a practical exemplification of a cross-coupling phenomenon in the atmospheric system.

SPECTRAL MAPPING THEOREM FOR ASCENT,ESSENTIAL ASCENT, DESCENT AND ESSENTIAL DESCENT SPECTRUM OF LINEAR RELATIONS

In [7], Cross showed that the spectrum of a linear relation T on a normed space satisfies the spectral mapping theorem. In this paper, we extend the notion of essential ascent and descent for an operator acting on a vector space to linear relations acting on Banach spaces. We focus to define and study the descent, essential descent, ascent and essential ascent spectrum of a linear relation everywhere defined on a Banach space X. In particular, we show that the corresponding spectrum satisfy the polynomial version of the spectral mapping theorem.

LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS

A closed linear relation T in a Banach space X is called left(resp. right) Fredholm if it is upper(resp. lower) semi Fredholm and its range(resp. null space) is topologically complemented in X. We say that T is left(resp. right) Browder if it is left(resp. right)Fredholm and has a finite ascent(resp. descent). In this paper, we analyze the stability of the left(resp. right) Fredholm and the left(resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered.

Dispersion Relation of Linear Waves in Quantum Magnetoplasmas

The quantum magnetohydrodynamic （QMHD） model is applied in investigating the propagation of linear waves in quantum magnetoplasmas. Using the QMHD model, the dispersion equation for quantum magnetoplasmas and the dispersion relations of linear waves are deduced. Results show that quantum effects affect the propagation of electron plasma waves and extraordinary waves （X waves）. When we select the plasma parameters of the laser-based plasma compression （LBPC） schemes for calculation, the quantum correction cannot be neglected. Meanwhile, the corrections produced by the Fermi degeneracy pressure and Bohm potential are compared under different plasma parameter conditions.

Factorization of Operators in Krein Spaces and Linear-Fractional Relations of Operator Balls

We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.

Thick-Film Negative-Temperature-Coefficient Thermistors with a Linear Resistance-Temperature Relation

The effect of the resistance R of Mn1.85Co0.3Ni0.85O4(MCN)thick-film negative-temperature-coefficient(NTC)thermistors on temperature T is studied carefully.Interestingly,the R–T relation is found to be decided simultaneously by the characteristic of the MCN oxide and the electrode structure of the NTC thermistor.For plane end electrodes,the R–T relation is nonlinear.However,for plane fork electrodes,the R–T relation can be linear.To clarify the intrinsic mechanism of the linear R–T relation,the electric field distribution in the MCN thick film is simulated.The obtained results suggest that the non-uniform electric field distribution between the electrodes is responsible for the R–T relation linearization.

Seasonal changes in the relationship between species richness and community biomass in grassland under grazing and exclosure, Horqin Sandy Land, northern China

How species diversityroductivity relationships respond to temporal dynamics and land use is still not clear in semi-arid grassland ecosystems. We analyzed seasonal changes of the relationships between vegetation cover, plant density, species richness, and above- ground biomass in grasslands under grazing and exclosure in the Horqin Sandy Land of northem China. Our results showed that in grazed and fenced grassland, vegetation cover, richness, and biomass were lower in April than in August, whereas plant density showed a reverse trend. Vegetation cover during the growing season and biomass in June and August were higher in fenced grassland than in grazed grassland, whereas plant density in April and June was lower in fenced grassland than in grazed grassland. A negative relationship between species richness and biomass was found in August in fenced grassland, and in grazed grassland the relationship between plant density and biomass changed from positive in April to negative in August. The relationship between the density of the dominant plant species and the total biomass also varied with seasonal changes and land use （grazing and exclosure）. These results suggest that long-term grazing, seasonal changes, and their interaction significantly influence vegetation cover, plant density, and bio- mass in grasslands. Plant species competition in fenced grassland results in seasonal changes of the relationship between species rich- ness and biomass. Long-term grazing also affects seasonal changes of the density and biomass of dominant plant species, which fur- tiler affects the seasonal relationship between plant density and biomass in grasslands. Our study demonstrates the importance of tem- poral dynamics and land use in understanding the relationship between species richness and ecosystem fianction.

Study on Variation of Fitting Goodness of Relation Between Earthquake Frequency and Magnitude before Moderately Strong Earthquakes (Ms≥5.0)

In this paper,characteristics of spatial and temporal variation of linear fitting goodness before some moderately strong earthquakes(Ms≥5.0)in the eastern part of China(east of longitude 180)are studied according to the famous Gutenberg-Richter’s relation expressed as lgN=a-bM,by using the moderate and small events that occurred in and around the source area.The results show that the linear goodness of fitting varies abnormally prior to these moderately strong earthquakes.In the early stage of the earthquake preparatory process,distribution of the energy released through small events in and around the source area is isostatic and the fitting goodness approximates 1,while the distribution of the energy turns to be isostatic before moderately strong earthquakes,leading to the obvious decrease of the linear goodness of fitting.This phenomenon could be a medium term anomaly and a medium term criterion for moderately strong earthquake prediction.

PDRK:A General Kinetic Dispersion Relation Solver for Magnetized Plasma

A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.

Estimation of peak relative velocity and peak absolute acceleration of linear SDOF systems

We have found some mistakes in the article by Jianwei Song et al. （2007）. The revisions are given below：

Dispersion Relations in Binary Gas Mixtures From a Kinetic Theory

Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourier-Laplace transform for model equations derived, the dispersion relations for both components are obtained.

RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.

HARDY-LITTLEWOOD-POLYA INEQUALITY FOR A LINEAR DIFFERENTIAL OPERATOR AND SOME RELATED OPTIMAL PROBLEMS

In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.

A new relative efficiency in parameter estimation for linear model

A new relative efficiency of parameter estimation for generalized Gauss-Markov linear model was proposed. Its lower bound was also derived. Its properties were explored in comparison with three currently very popular relative efficiencies. The new relative efficiency not only reflects sensitively the error and loss caused by the substitution of the least square estimator for the best linear unbiased estimator, but also overcomes the disadvantage of weak dependence on the design matrix.

基于GRA-GRU的淮河流域水质预测研究

水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域水质数据为样本,使用线性插值修补缺失数据和剔除的异常数据。使用灰色关联分析计算不同水质指标间的相关性,选择高相关性的水质指标以确定输入变量,并使用门控循环单元(Gated Recurrent Unit, GRU)预测不同的水质指标。将GRA-GRU的预测结果与反向传播神经网络(Back Propagation Neural Network, BPNN)、循环神经网络(Recurrent Neural Network, RNN)、长短期记忆神经网络(Long Short Term Memory, LSTM)、GRU及灰色关联分析-长短期记忆神经网络(Grey Relational Analysis-Long Short Term Memory, GRA-LSTM)进行对比分析,结果显示GRA-GRU在不同水质指标预测上具有较好的适应性,可以有效降低预测误差。其中,与其他模型相比,GRA-GRU预测的化学需氧量在均方根误差上分别降低了3.617%、0.681%、0.478%、1.505%和0.471%。

国六缸内直喷轻型汽油车污染物劣化特性

为了更加准确地了解轻型汽油车的排放劣化特征,选取了6辆缸内直喷轻型汽油车,进行160 000 km里程累积,分析气态污染物CO、THC、NO_(x)的排放随行驶里程的劣化规律。结果表明,CO、THC、NO_(x)三种污染物的平均劣化系数分别为2.1、1.9和1.3,CO、THC、NO_(x)三种污染物的平均劣化修正值分别为121.8、9.4、3.3。自然吸气车辆污染物和里程的线性关系较涡轮增压车辆更加明显,R^(2)都高于0.5;涡轮增压车辆除了THC的线性拟合较好,CO、NO_(x)与里程的线性关系都较差,出现了明显的波动。有利于准确估算轻型汽油车的尾气排放量,进一步加严机动车污染排放限值,促进空气质量改善。

基于无人机多光谱影像的棉花苗期株数提取方法

准确、快速获取棉花苗期株数对棉花管理早期决策起着至关重要的作用。文中利用无人机遥感获取棉花苗期多光谱影像,通过植被指数NDVI剔除土壤、地膜等背景,再进行灰度运算、阈值分割、形态学变换等图像处理操作提取棉苗轮廓,并运用OpenCV图像识别计数方法得出棉苗数量,统计误差在0.23%~1.45%之间。结合地面调查,采用线性回归分析方法,建立无人机图像识别株数与实际株数的线性关系模型。结果表明,模型精度指标R^(2)、RSME和nRSME分别为0.9865、1.6124和2.137%。该方法可为后续田间大面积测定出苗率和棉花高产的准确评估提供技术支持。

Atomic Dispersed Hetero‑Pairs for Enhanced Electrocatalytic CO_(2)Reduction

Electrochemical carbon dioxide reduction reaction(CO_(2)RR)involves a variety of intermediates with highly correlated reaction and ad-desorption energies,hindering optimization of the catalytic activity.For example,increasing the binding of the*COOH to the active site will generally increase the*CO desorption energy.Breaking this relationship may be expected to dramatically improve the intrinsic activity of CO_(2)RR,but remains an unsolved challenge.Herein,we addressed this conundrum by constructing a unique atomic dispersed hetero-pair consisting of Mo-Fe di-atoms anchored on N-doped carbon carrier.This system shows an unprecedented CO_(2)RR intrinsic activity with TOF of 3336 h−1,high selectivity toward CO production,Faradaic efficiency of 95.96%at−0.60 V and excellent stability.Theoretical calculations show that the Mo-Fe diatomic sites increased the*COOH intermediate adsorption energy by bridging adsorption of*COOH intermediates.At the same time,d-d orbital coupling in the Mo-Fe di-atom results in electron delocalization and facilitates desorption of*CO intermediates.Thus,the undesirable correlation between these steps is broken.This work provides a promising approach,specifically the use of di-atoms,for breaking unfavorable relationships based on understanding of the catalytic mechanisms at the atomic scale.