MULTIPLICATIVE GROUP AUTOMORPHISMS OF INVERTIBLE UPPER TRIANGULAR MATRICES OVER FIELDS

Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).

A model supported by GIS for locating and quantifying PM_(2.5) emission originated from residential wood burning

A research method was presented for spatially quantifying and allocating the potential activity of a fine particle matter emission （ PM2.5 ）, which originated from residential wood burning （RWB） in this study. Demographic, hypsographic, climatic and topographic data were compiled and processed within a geographic information system（GIS）, and as independent variables put into a linear regression model for describing spatial distribution of the potential activity of residential wood burning as primary heating source. In order to improve the estimation, the classifications of urban, suburban and rural were redefined to meet the specifications of this application. Also, several definitions of forest accessibility were tested for estimation. The results suggested that the potential activity of RWB was mostly determined by elevation of a location, forest accessibility, urban/non-urban position, climatic conditions and several demographic variables. The linear regression model could explain approximately 86% of the variation of surveyed potential activity of RWB. The analysis results were validated by employing survey data collected mainly from a WebGIS based phone interview over the study area in central California. Based on lots free public GIS data, the model provided an easy and ideal tool for geographic researchers, environmental planners and administrators to understand where and how much PM2.5 emission from RWB was contributed to air quality. With this knowledge they could identify regions of concern, and better plan mitigation strategies to improve air quality. Furthermore, it allows for future adjustment on some parameters as the spatial analysis method is implemented in the different regions or various eco-social models.

Improving the Design of Children's Books Art and Design Applied to Books——Research in the UK

This article is mainly on the research of how to improve the design of children's books.

Drought and Waterlogging Characteristics during the Growth Period of Summer Maize in Luxi Plain Areas

In summer maize growth period,the water supply and demand ratio is regarded as the evaluation index of drought and waterlogging for the summer maize in Liaocheng City. Using GIS,statistics,agrometeorology and other methods,we analyze the precipitation during the summer maize growth period in Luxi Plains from 1961 to 2011. Through the calculation of drought and waterlogging index,it indicates that the disasters of drought and waterlogging frequently occur during the summer maize growth period,mainly affected by the drought; the frequency of occurrence of drought accounts for 80. 4%,that is,it is very prone to serious drought phenomenon,seriously affecting the normal growth and development of summer maize during the seedling period. With global warming,the industrial and domestic water demand is increasing year by year,so it is extremely difficult to increase the water diversion to solve the problem of water shortage for the growth of summer maize. Finally we put forth the following recommendations:( i) Selecting drought-resistant varieties,and improving the water resource use efficiency;( ii)Promoting the water and fertilizer coupling,sprinkler irrigation,drip irrigation,micro-irrigation and other water-saving irrigation technologies,and improving the water use efficiency;( iii) Promoting the ditch,ridge and laminating cultivation technology,reducing the field evapotranspiration,keeping warming and conserving moisture,and saving water resources;( iv) Strengthening the construction of water conservancy facilities,so that it can be irrigated during drought and drained during waterlogging;( v) During dry season,timely organizing artificial rainfall operation,and increasing precipitation in arid areas to ease drought;( vi) Rationally exploiting the groundwater,and improving the underground water use efficiency.

An Efficient CSI Feedback Scheme for Dual-Polarized MIMO Systems Using Layered Multi-Paths Information

Massive MIMO is one of tile enabling technologies tbr beyond 4G and 5G systems due to its ability to provide beamforming gain and reduce interference Dual-polarized antenna is widely adopted to accommodate a large number of antenna elements in limited space. However, current CSI（channel state information） feedback schemes developed in LTE for conventional MIMO systems are not efficient enough for massive MIMO systems since the overhead increases almost linearly with the number of antenna. Moreover, the codebook for massive MIMO will be huge and difficult to design with the LTE methodology. This paper proposes a novel CSI feedback scheme named layered Multi-paths Information based CSI Feedback （LMPIF）, which can achieve higher spectrum efficiency for dual-polarized antenna system with low feedback overhead. The MIMO channel is decomposed into long term components （multipath directions and amplitudes） and short term components （multipath phases）. The relationship between the two components and the optimal precoder is derived in closed form. To reduce the overhead, different granularities in feedback time have been applied for the long term components and short term components Link and system level simulation results prove that LMPIF can improve performance considerably with low CSI feedback overhead.

Nonlinear Oscillation Analysis by an Orthogonal Function Method

In this paper an orthogonal function method is presented based on the idea to suppose perioche sohuion with the method of harmonie balance The displaeement is expressed in the form of trigonometric fumctions a group of simplified digenequationsare obtained by the use of orthogonarity of trigonometric fumetions and linear mondes The method overcomes the diffieulty of a drifi term existing in systems with quadratic nonlinearities .The ealeulation examples show that the method has thd advantages of high caleulation preeision high convergenee speed and littld ealeulation work

AN OPERATOR-SPLITTING ALGORITHM FOR ADVECTION-DIFFUSION-REACTION EQUATION

An operator-splitting algorithm for three-dimensional advection-diffusion-reaction equation is presented.The method of characteristics is adopted for the pure advection operator, the explicit difference scheme is used for diffusion,and a prediction-correction scheme is em- ployed for reaction.The condition for stability of the algorithm is analysed.Severall inear and nonlinear examples are illustrated to test the convergence and accuracy of the numerical proce- dure,and satisfactory agreements between computed and analytical solutions are achieved.Due to its simplicity,stability,and validity for both one-and two-dimensional problems,the success- ful algorithm can be used to numerical simulations of viscous fluid flows,the transport of pollu- tants and sedimentations in reservoirs,lakes,rivers,estuaries and other environments,cooling- problems in heat or nuclear power plants,etc.

Wave Propagation Simulation Using the CIP Method of Characteristic Equations

We apply the CIP(Cubic Interpolated Profile)scheme to the numerical sim-ulation of the acoustic wave propagation based on characteristic equations.The CIP scheme is based on a concept that both the wavefield and its spatial deriv ative propa-gate along the same characteristic curves derived from a hyperbolic differential equa-tion.We describe the derivation of the characteristic equations for the acoustic waves from the basic equations by means of the directional splitting and the diagonaliza-tion of the coffcient matrix,and establish geophysical boundary conditions.Since the CIP scheme calculates both the wavefield and its spatial derivatives,it is easy to realize the boundary conditions theretically.We also show some numerical simula-tion examples and the CIP can simulate acoustic w ave propagation with high stability and less numerical dispersion.The method of characteristics with the CIP scheme is a very powerful technique to deal w ith the wave propagation in complex geophysical problems.