Journal of Jishou University(Natural Sciences Edition)

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Conjugacy Classes of Elements of Order 2 in GL(2,Q)

YOU Xing-Zhong, CHEN Wei-Min, PENG Da-Qian

journal6 2010, 31 (1): 1-3.

Abstract （1930）

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By an elementary proof,conjugacy classes of elements of order 2 in the general linear GL(2,Q) are determined in this paper.

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On the Cardinalities of Row Space of Some Special Boolean Matrices

ZHONG Li-Ping, DENG Jian

journal6 2010, 31 (1): 4-6.

Abstract （2460）

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Let Bm×n be the set of all m×n Boolean matrices;R(A) denote the row space of A∈Bn,|R(A)| denote the cardinality of R(A),m,n be positive integers,and k be non negative integers.In this paper,we prove the following three results:(1) let A∈Bn×n,m,(ⅰ) if A is the idempotent matrix,i.e.,A2=A,then |R(Am)|=|R(A)|;(ⅱ) if A is the involutory matrix,i.e.,A2=I,then |R(Am)|=|R(A)| when m is an odd number or |R(A)|=2n when m is an even number;(2) let A∈Bm×nbe k of the numbers of 1,0≤k≤min{m,n},and each row and column is at most one of the numbers of 1 in A,then |R(A)|=2k; (3) let A∈Bn×n be the partitioned matrix as A=(O OO A1),A1=(aij)k×k,aij=0(i>j),aij=1(i≤j),i,j=1,2,…,k,then |R(A)|=k+1.

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Some Classes of Upper Embeddable Graphs

LIU Duan-Feng

journal6 2010, 31 (1): 7-8.

Abstract （2016）

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Using some special properties of graphs,such as the vertex-set of a graph with a C- division,every
edge of a graph belonging to a 3-circle,the graph without cut-vertex and so on,the author studies the maximum genus of graphs,and obtains a class of upper embeddable graphs.

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Positive Solutions for Multiple-Point Boundary Value Problem of Fractional Differential Equations

ZHONG Wen-Yong

journal6 2010, 31 (1): 9-12.

Abstract （2267）

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This paper deals with the existence of positive solutions for multiple-point boundary value problem of fractional differential equations.In light of fixed-point theorems,some sufficient conditions are obtained to guarantee the existence of at least one or three positive solutions of the boundary value problems.

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Properties of the Charactristic of Hamilton-Jacobi Equations I

ZHAO Yin-Chuan

journal6 2010, 31 (1): 13-15.

Abstract （1897）

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This paper is concerned with the Hamilton-Jacobi (HJ) equations of multidimensional space variables with convex Hamiltonians.The author proves the extreme curve in the formula of the solution to the HJ equation is a characteristic and for each point in upper half-space,there exists a valid characteristic segment passing through it.

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Algorithm for General Quadratic Quaternionic Equations with One Unknown

CHENG Xue-Han, LU Xiao-Yun

journal6 2010, 31 (1): 16-18.

Abstract （2659）

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By applying corresponding theories of linear equation,we give the basic steps of solving the general quadratic quaternionic equation with one unknown.

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Continuous Properties of BSDE with Stochastic Lipschitz Condition

SONG Li

journal6 2010, 31 (1): 19-21.

Abstract （2357）

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This paper investigates the continuous properties of solutions of backwards stochastic differential equation with stochastic Lipschitz condition.By aprior estimate of solutions,the continuous properties of BSDE are obtained according to terminal data and generator.

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Polynomial Preconditioning Technique for Matrix Equation

TIAN Jing, ZHOU Fu-Zhao, ZHONG Zhi-Hong

journal6 2010, 31 (1): 22-26.

Abstract （2951）

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Firstly the polynomial preconditioning technique and an interpolation polynomial method are considered for constructing a proper polynomial preconditioners to transform the system.This reduces the distribution range of singular value and improves the ratio of singular value.Besides,a new algorithm is given and the convergence of the algorithm is analysed.The expression of estimation about convergence rate testifies that this algorithm can improve the convergence rate of iterative methods significantly if a appropriate preconditioning matrix is used.The numerical experiments show that the preconditioning matrix is more effective in convergence of algorithm than the original matrix.The superiority of the preconditioning matrix in solving speed is demonstrated.Therefore,the feasibility of the algorithm is illustrated.

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Generalzation of Matching Problem

LI Ya-Lan

journal6 2010, 31 (1): 27-29.

Abstract （2229）

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By increasing the condition,the matching problem is extended from two different perspectives,and then a series of important results were obtained.

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Semi-Fragile Watermarking Scheme Based on DCT and DHT

ZHOU Jian-Qin, SHANG Guan-Cheng

journal6 2010, 31 (1): 30-34.

Abstract （2552）

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A semi-fragile watermarking scheme needs robustness to some common attacks and capability of checking tamper.The combination of DCT and DHT is analyzed.From the analysis,a novel semi-fragile watermarking scheme is presented.In this scheme,the host image is first transformed by DCT,then some region of low or middle frequency coefficients is chosen to be transformed by DHT.Last,the watermark is embedded into the region.The watermark embedded into the low or middle frequency coefficients is robust.After the two transforms,there are some host image features in the transformed region so that the tampered region and sort of watermarked image can be reflected.Simulation results show that it is effective.

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Applications and Prospect of Ant Colony Algorithms

YE Zhi-Wei, ZHOU Xin, XIA Bin

journal6 2010, 31 (1): 35-39.

Abstract （6998）

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Ant colony algorithm is a novel category of bio-inspired algorithm for optimization engineering problems.Firstly of all,the basic principle and model of ant colony algorithm are introduced.Then,a series of schemes on improving the ant colony algorithm are discussed,and the new applications are also provided.Finally,some remarks on the further research and directions are presented．

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Simulation of Convolutional Rate Matching Algorithm for TD-SCDMA

ZHU Hong, BAI Wen-Le

journal6 2010, 31 (1): 40-42.

Abstract （2620）

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Rate matching is an important part in channel encoding and multiplexing of TD-SCDMA.Semi-static attribute is an important parameter in rate matching algorithm.This paper analyses convolutional coding rate matching principle for TD-SCDMA and completes the software simulation of convolutional rate matching algorithm.Simulation demonstrates that the realization of the program is feasible and semi-static attribute is to adjust the proportion of repeated or punctured data for each TrCH.

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Design of Fuzzy RBF Neural Network Based on Genetic Algorithm and its Application

DUAN Ming-Xiu

journal6 2010, 31 (1): 43-46.

Abstract （2645）

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A fuzzy RBF neural network learning algorithm based on genetic algorithm is proposed.This algorithm adopts genetic algorithm to optimize the fuzzy RBF neural network’s structure parameters,adapts the optimization result as the initial value of the fuzzy RBF neural network’s structure parameters,and dynamicly adjusts the parameters using the gradient decent methods.Finally the algorithm is applied to classify the data and function approximation.The simulation shows that the fuzzy RBF neural network has higher precision and robustness.

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Some New Researches of Field Theory in Mathematics and the Applications in Physics

ZHANG Yi-Fang

journal6 2010, 31 (1): 47-53.

Abstract （2910）

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When the space-dimension of mathematics and the rank n of calculus are extended to fraction and various number-systems,the field theory and its formulas may be correspondingly extended.In these cases,Gauss law and Stokes law,and corresponding the extensions on gradient,divergence and curl are searched,in which there may be different forms of extensive curl.It may combine the fractal and complex-dimension.Moreover,the applications in physics are researched.The development from scalar and vector to tensor,spinor and twistor,etc.is stated briefly.

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Center of Mass Motion of Trapped Ions under Control of Traveling-Wave

JIANG Min, WU Yun-Wen, YI Jian

journal6 2010, 31 (1): 54-57.

Abstract （1828）

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A two-ion system is studied,in which the trapped ions couple to a traveling-wave laser field.The authors analyze the influence aroused by different initial conditions and the trap frequencies as well as interaction time by taking numerical calculation and computer simulation methods.Meanwhile,the authors plot the orbits on phase space,and propose that the external parameters and initial conditions of trapped ions are the external influential factors for regular and chaotic motion of the trapped ion.

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Neutrino Paradox’s Solution and its Support for Hawking’s Positivism

LI Qing-Yan

journal6 2010, 31 (1): 58-60.

Abstract （2393）

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In the late 1960s，U.S.astrophysicist Davis successfully detected the solar neutrino.However,the number of income was only about half of the standard solar model predictions.According to unified electro-weak theory,the neutrino has zero rest mass,which constitutes a paradox of solar neutrinos.Kam-Lan Experimental results showed that atmospheric neutrino oscillation did occur,and neutrinos did have rest mass.The follow-up sudbury experiments finally resolved the issue of neutrino paradox,making people question unified electro-weak theory,think about their significance in particle physics as well as in astrophysics.Those objectively support the self-consistent logical positivism.

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Construction of Biorthogonal Wavelet Based on the Perfect Reconstruction Condition

XIONG Qi, ZHOU Shao-Hua, LI Rui-Min, WANG Zhen-Dao, ZENG Jian-Ping

journal6 2010, 31 (1): 61-63.

Abstract （2614）

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A general construction approach of biorthogonal wavelet filters based on the perfect reconstruction is presented.Given the number of vanishing moments and length of the filters,coefficients of biorthogonal wavelet filters can be obtained by the resolution of equations.This method is used to construct JPEG2000 5/3 wavelet,CDF9/7 wavelet and a biorthogonal 9/7 taps wavelet which is adaptive to hardware implement with simple coefficients.

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A New Ultimate Strength Calculating Method for Arbitrary Cross-Section Under Bieccentric Loading with Meshless Method

YANG Yu-Dong, ZHANG Ke, WU Min-Zhe

journal6 2010, 31 (1): 64-69.

Abstract （2268）

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In order to analyze the cross-section bearing capacity of bi-eccentric compressive short-limed shear wall,the authors designed the analyzing program of bi-eccentric cross-section bearing capacity.Based on the interpolation principle.The program calculates the inward pressure of concrete fully according to the accurate solution of integral region obtained by mathematical equation,so as to avoid the errors of mesh generation.The program results agree well with the exprimental results.This method provides a new idea to develop similar program.By using that program,the interrelated curved surface N-M of bi-eccentric compression of short-limbed shear wall is obtained,and it is found that the equiaxed force line is similar to special-shaped column.The program can fully grasp the cross-section bearing capacity of bi-eccentric compressive short-limbed shear wall,and thus it can meet the requirements of engineering design.

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Design of AT89S52-Based Shaft Temperature and Humidity Intelligent Control System

LI He-Ping

journal6 2010, 31 (1): 70-72.

Abstract （2734）

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The system adopts temperature sensor DS18B20 and humidity sensor HM1500 to carry out high-accuracy detecting on shaft environment.AT89S52 monolithic machine is used to carry out the intelligent control on the temperadity and humidity.System interposes the systematic intelligence of thermoregulation switch so that it can expand outside facilities and realize the communication of RFID to provide a guarantee to the shaft personnel's safety.

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Optimization Research of Isosurface in Marching Cubes Algorithm

LI Gai

journal6 2010, 31 (1): 73-77.

Abstract （2523）

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The optimization operation of isosurface is very common in the three-dimension reconstruction.In this paper,the author uses middle point choice to replace lineal insert-value and the method of making a strip of triangle to optimize the form and the storage structure of the triangle in the isosurface，thus improving drawing speed of three-dimension models greatly.

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Synthesis of BaTiO3 Nanoparticle with Organic Base by Hydrothermal Method

WANG Hong-Jun, KOU Hui-Zhi, WANG Ji-Chao, XUE Hong-Bin, ZENG Cui-Ping, YANG Shu-Ming

journal6 2010, 31 (1): 78-82.

Abstract （3168）

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Nanocrystalline barium titanates were synthesized using a hydrothermal method with tetramethyl ammonium hydroxide as the mineralizer.The effects of the sources of barium,concentration of Ba2+ ions,pH of precursor solutions,reaction time and temperature on the formation of BaTiO3 nanoparticles were investigated.It was shown that monodispersed monolithic BaTiO3 nanoparticles and purer samples could be prepared pretty easily with the application of the organic base of tetramethyl ammonium hydroxide.Monolithic BaTiO3 nanoparticles of various sizes could be synthesized by the adjustment of reaction conditions.

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Synthesis of Cyclohexyl Propionate Catalyzed by Ferric Sulfate Hydrate Under Microwave Irradiation

CHEN Xiao-Yuan, ZHOU Yi-Bo, WU Xian-Wen

journal6 2010, 31 (1): 83-86.

Abstract （2146）

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Cyclohexyl Propionate was directly synthesized by propionic acid and cyclohexanol with ferric sulfate hydrate as the catalyst under microwave irradiation.The effects of microwave irradiation power,irradiation time,reactant ratio,amount of catalyst and amount of watercarrying agent on the yield of cyclohexyl propionate were systematically studied.Research results showed that the optimum reaction conditions were as follows:microwave irradiation power was 700 W,fixed amount of propionic acid was 0.05 mol,the ratio of cyclohexanol to propionic acid was 3∶1,the amount of catalysts was 1.5 g,and cyclohexane as the water-carrying agent was 6 mL,after 30 min reaction,the yield of cyclohexyl propionate reached 94.4%.

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Physico-Chemical Properties of Hydrolysis Products from Channel Catfish Skin

HUANG Cheng, CAO Guang-Hui, YIN Hong, LI Yong-Ping, LIU Zhen-Cheng

journal6 2010, 31 (1): 87-90.

Abstract （2147）

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Hydrolysis products of channel catfish skin was extracted by using acetic acid method and acetic acid + papain method,and their physico-chemical properties were described.Results showed that the denaturation temperatures of acid-soluble hydrolysis products and acetic acid + papain hydrolysates were at 30~35 ℃ and 28~35 ℃ respectively.The dissolubility,emulsify capacity and emulsifying stability of products obtained by acetic+papain method were superior to that obtained by acetic acid method,but the latter produced a better water absorption capacity,oil absorption capacity,foaming capacity and foam stability than the former.

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Wet Method Preparation and Electrochemical Characterization of Li₄Ti₅O₁₂/Graphite Anode Material

HE Ze-Qiang, XIONG Li-Zhi, LIANG Kai

journal6 2010, 31 (1): 91-95.

Abstract （2177）

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Li₄Ti₅O₁₂/graphite composite was prepared by sol-gel method using ethyl alcohol as solvent,lithium acetate and tetrabutyl titanate and graphite as raw materials.Li₄Ti₅O₁₂/graphite composites were characterized by X-ray diffraction(XRD),scanning electron microscopy (SEM) combined with electrochemical tests.Results show that Li₄Ti₅O₁₂/graphite composite with 5% carbon mass fraction containing can be obtained by annealing the precursor at 600 ℃ for 6 h in Ar atomophere.The composites can deliver a specific capacity of 167.1 mAh/g,99.0% and 105.1% of the capacity can be retained after discharged for 80 times at 0.1 C and 2.0 C,respectively.Compared with pureLi₄Ti₅O_12,Li₄Ti₅O₁₂ /graphite composite shares larger discharge capacity,better cyclability and rate performance,suggesting Li₄Ti₅O₁₂/graphite composite is a promising anode material for lithium ion batteries.

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Evaluation of the Ecological Safety of Transgenic Carp by AFLP

TONG Guang-Xiang, KUANG You-Yi, LIANG Li-Qun, SUN Xiao-Wen, CAO Ding-Chen

journal6 2010, 31 (1): 96-103.

Abstract （2342）

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The genome of first filial generation,whose parents were carp with different rate of transferred Oncorhunchus Suckley growth hormone gene,were scanned to estimate its eco-security,using the wild carp of Fu-yuan,common carp of Songhua River of Harbin and cultural carp as control.Control group,1% experimental group,10% experimental group,25% experimental group,50% experimental group,60% experimental group,H group and Y group were amplified with 10 pairs of AFLP primers.663 locus were obtained.The numbers of poly-bonds locus were all more than 50% in every population.With the rate of transgenic parents increasing,the numbers of filial generation polymorphism locus descended.Number of alleles (Na),effective number of alleles (Ne),Nei’s gene diversity (H),Shannon’s Information index (I),genetic inter-group similarity (S),genetic distance(D),the coefficient of gene differentiation among populations within species (Gst) and gene flow (Nm) were calculated with PopGen32 software.Ten groups were compared.The results showed that the largest value of Na,Ne,Nei’s gene diversity index (H) and Shannon information index (I) were all in Y group,and the second,in the control groups.The minimum were in the H group.In five filial generation experimental groups of transgenic parents of different rate,with the rate of trans-gene parents increasing,all the four indexes tended to descend.Genetic inter-group similarity (S) and genetic distance (D) showed that 25%,50% and 60% experimental group were separated from other groups in different degree.Especially,the 60% experimental group was dramatically far away from the same group.It is thus evident that 60% experimental group had great difference with the others.The comparing result of the five trans-gene experimental groups,H group and Y group Gst and gene flow showed that gene differentiation was larger and gene flow was small.With the rate of trans-gene parents increasing,the Gst of filial generation increased and the gene flow descended.From those,it can be seen that the genome of the first filial generation changed in a certain regularity with the increase of parents transgenic rate.All of these illuminate that more transgenic fish escape,more influence to the wildlife population.Transgenic fish should be prevented from escaping to reduce the genome pollution of wildlife population.

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Investigation of Enhancement and Releasement Effect ofFishery Stock in Gaoqiao Mangrove

YE Ning, YANG Feng, YE Jian-Xin, LIN Guang-Xuan

journal6 2010, 31 (1): 104-109.

Abstract （2599）

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50 000 mono-sex individuals of Nile tilapias were released in the mangrove area of Hongkan and Bohe to evaluate the releasing effects on the fishery resources.By fixed point sampling survey,both the current year catch and diversity increased after releasement but both declined in the regions without releasement;the number of commercial fishes increased after releasement;the released mono-sex(male) Nile tilapias didn’t propogate,and they just swimmed about in certain regions.After released,Nile tilapias accounted for 32% of the total number and 36.2% of gross weight in fish harvest.The survival rate of released Niles tilapia was 72%.The saccumulated growth rate of Niles tilapias was 23.25 g/month.A regression combined analysis of the two results above,some parameters were calculated:K=0.242 6,L∞＝21.565 13 cm,t＝9.24 months,W∞＝155.84 g.Preliminary effect of releasement is achieved.

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Key Technology and Benefit Analysis of Intensive Breeding of the Cross Breeds of Boer Goat

LIU Chao, WANG Xiang-Lin, ZHANG Ren-Fu, WANG Qing-Lin

journal6 2010, 31 (1): 110-112.

Abstract （2226）

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The experience of the successful intensive breeding of goats in Xiangxi autonomous prefecture of tujia and miao minorities in recent years is summarized.The key technology of intensive breading of the cross breeds of Boer goat is put forward,and the benefit is analyzed.The study is beneficial to further the development of goats industry in mountain areas.

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Effect of Salvia Miltiorrhiza Injection on CRP and Adhesion Molecule in the Type Ⅱ Diabetic Nephropathy Patient Blood

PENG Qin, XIANG Min, LONG Shu-Yun, CHEN Li-Li

journal6 2010, 31 (1): 113-115.

Abstract （2380）

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To observe the effect of salvia miltiorrhiza injection on CRP,P-sel and ICAM-1 in the blood of Type Ⅱ diabetic nephropathy patient and to approach the mechanism of conbined treatment of traditional Chinese medicine and Western medicine for the type Ⅱ diabetic nephropathy，salvia miltiorrhiza injection was applied to treat 38 patients with typeⅡ diabetic nephropathy,and another 43 patients were used as contrasts treated by routine Western medicine.The content of CRP,P-sel and ICAM-1 in the blood of patients were detected both before and after the treatment.The results showed that the total effective rate of salvia miltiorrhiza injection treatment for type Ⅱ diabetic nephropathy was 68.4%,and that of the contrast group was 46.5%.There was significant difference between them.Before treatment the levels of CRP，P-sel and ICAM-1 between salvia miltiorrhiza injection group and Western medicine contrast group had no significant difference,but after treatment there was statistical difference between them,and the levels of CRP，P-sel and ICAM-1 molecule in the group cured by salvia miltiorrhiza injection were lower than that of contrast group.It can be concluded that there is significant curative effect of salvia miltiorrhiza injection treatment for type Ⅱ diabetic nephropathy patients.Probably the mechanism of treatment is that salvia miltiorrhiza injection can down regulate inflammatory cell activity and inhibite inflammatory reaction.

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Problems of Ethnic Cultural Tourism Property in Xiangxi and Countermeasures

LIU Xun-Hua

journal6 2010, 31 (1): 116-120.

Abstract （2497）

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There are several problems in Xiangxi ethnic cultural tourism property:unclear property rights,weak property conciousness,lack of brand awareness and innovation,and too much resemblance between products.To solve those problems,we should strengthen the protection of cultural tourism property,improve product and industry innovation,and promote the government-led strategy.

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Analysis on Cause of Irrational Behavior of Tourist’s Decision-Making

ZHU Hu-Ying

journal6 2010, 31 (1): 121-124.

Abstract （2594）

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Along with tourism developing and standard of living advancing,tourism consumption turns into an important part of consumption.People canonize rational behavior of tourist’s decision-making,but numerous tour information and diversification of tourism demand make it more difficult,and irrational behaviors of tourist’s decision-making becomes more prevalent.The characteristics of irrational behaviors of tourist’s decision-making are unilateralism of collecting information,blindness of discriminating information,simplicity of choosing tour forms,irrationality to choose tour consumption structure,character of herding behaviors at choosing tourism products.The causes of irrational behaviors of tourist’s decision-making are analyzed with Behavioral Economics theory.As a result,to reduce irrational behaviors of tourist’s decision-making,we should normalize tour information,design reasonable tour products,cultivate healthy tour habits,advance tourism standard of behavior decision-making.

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Statistic Analysis of Foundation Papers in Core Periodicals of Pharmacy Sciences

LIU Xiao-Feng, YANG Mao-Sheng

journal6 2010, 31 (1): 125-128.

Abstract （2368）

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Based on 6746 foundation papers in 17 core periodicals of pharmacy sciences in 2008,the authors perform a statistic analysis on the relevant information contained in the text using bibliometrics method. The findings reported in this article will be helpful to understand the characteristics and status of Chinese journals of pharmaceutical sciences.

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Characterization for Rings Without Zero Divisor andExamples of Various Rings

CHEN Xiang-en

journal6 2010, 31 (2): 1-2.

Abstract （2369）

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The equivalence conditions for characterizing rings without zero divisor are summarized and the examples of various rings are given in this paper.

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Finite Direct Sums of (Weak) (n,d)-Rings and n-Coherent Rings

LI Wei-Qing, OuYang-Bai-Yu

journal6 2010, 31 (2): 3-6.

Abstract （2140）

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Let R1,R2,…,Rm be rings.It is proved that (1) mi=1Ri is a right (n,d)-ring (resp. weak (n,d)-ring,n-coherent ring) if and only if each Ri is a right (n,d)-ring (resp. weak (n,d)-ring,n-coherent ring);(2) rD（mi=1Ri) =sup{rD(R1),rD(R2),…,rD(Rm)};(3) wD(mi=1Ri) = sup{wD(R1),wD(R2),…,wD(Rm)}.

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Oscillation of Even Order Half-Linear Neutral Delay Differential Equation

HAN Zhen-Lai, SUN Yi-Bing, LI Tong-Xing, SUN Shu-Rong

journal6 2010, 31 (2): 7-9.

Abstract （2820）

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By means of Riccati transformation and averaging technique,this paper establishes new oscillation criteria for even order half-linear neutral delay differential equation.

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Development from Bernoulli Inequality to Hlder Inequality and Its Applications

XING Jia-Sheng, WANG Hong-Zhi

journal6 2010, 31 (2): 10-14.

Abstract （2714）

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This paper presents the proof of geometric mean and arithmetic mean inequality by Bernoulli inequality.Then it gives the proof of Young inequality and gets the elementary proof of Hlder inequality.And some important inequalities can be proved by those results.

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Improvement of Hilbert’s Type Integral Inequality with Some Parameters

SHANG Xiao-Zhou, HE Le-Ping

journal6 2010, 31 (2): 15-17.

Abstract （2254）

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Some improvements of Hardy-Hilbert’s integral inequality are given by means of a sharpening of Hlder’s inequality.Some new inequalities are established.

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Area of a Polygon and Double Integration of a Complex Function

HUANG Yi-Ru, XU Cheng-De, ZHU Xiao-Yun, LIU Yan-Ping

journal6 2010, 31 (2): 18-21.

Abstract （2053）

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The authors deduce a formula of the area of a grid point ploygon in the form of complex double integration by means of a formula of the area of a grid point polygon in number theory.In addition the authors derive the formula of integral round a contour via the expression of the area of polugon in analytic set form.And the complex double integration is studied briefly.

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Construction of Properly Posed Set of Nodes for Interpolation in the Π_k(R²) Space

XU Yan, CHEN Wei, CUI Li-Hong

journal6 2010, 31 (2): 22-24.

Abstract （2202）

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The Lagrange interpolation of Π_k(R²) space is studied.The method of constructing the properly posed set of nodes for Lagrange interpolation in the Π_k(R²)space is given,and this generalizes the main method of constructing the properly posed set of nodes for Lagrange interpolation in the Π_k(R²) space which was acquired by Ward Cheney and Will Light in “The tutorial of approximation theory”.Thus a general conclusion is obtained.

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Normal Families of Meromorphic Functions Concerning Multiplicity of Zeros

DING Jian-Jun, GU Rong-Mei, YUAN Wen-Jun

journal6 2010, 31 (2): 25-28.

Abstract （2442）

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A normality criterion of meromorphic functions is proved:let F be a family of functions meromorphic in a domain D,n,m,k be three positive integers such that n≥m+1 and a≠0,and b be two finite complex numbers.If for each f∈F,all zeros of f have multiplicity at least k+1,and fm+a(f(k))n≠ b in D,F is normal in D.

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Posteriori Error Estimates for Mixed Finite Element Solutions of Optimal Control Problems

FU Min, DIAO Lin, LUO Chao-Liang

journal6 2010, 31 (2): 29-32.

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An a posteriori error analysis is obtained for mixed finite element approximation of quadratic convex optimal control problem governed by nonlinear elliptic equation.The state and the co-state are approximated by the k-th R-T mixed finite element spaces and the control is approximated by piecewise constant functions.The results are based on the approximation for both the state variables and the control variable.In numerical experiments,the posteriori error estimators are used as the mesh refinement indicator.Then it is clear that the adaptive finite element method is more efficient.

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