Journal of Jishou University(Natural Sciences Edition)

The Number of Solutions of Simultaneous Pell Equations

LE Mao-Hua

journal6, 2003, 24(2): 1-9.

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Let a,b　be distinct positive integers.If max (a,b)＞ 10118,then the simultaneous Pell equations x2-ay2=1 and z2-by2=1 have at most two positive integer solutions (x,y,z).

Existence of Positive Solutions for Some Nonlinear Third-Order Two-Point Boundary Value Problems

YAO Qing-Liu

journal6, 2003, 24(2): 10-14.

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The existence of positive solution to some two-point boundary value problems are considered for third-order nonlinear ordinary differential equation.This class of boundary value problems arises from the investigation for flow of sticky liquid and possesses wide application in liquid mechanics.In recent years,Professor Jiang Daqing has obtained the existence of positive solution under the condition where nonlinear term is superlinear or sublinear.By improving the method used by Jiang,the author give two existence theorems of the class of problems under the condition where the nonlinear term is neither superlinear nor sublinear.The processes are as follows: (1) By applying the Green functions of corresponding boundary value problems the problems are transformed to integral equations on the space of continuous functions; (2) By applying the properties of Green functions the suitable cones are chosen; (3) By making use of Krasnoselskii fixed point theorem of cone expansion-compression type,two existence theorems of positive solution are obtained.This paper implies that Jiang’s main conclusions are the special cases of our results.

The Attractors and Fractal Images in the Complex Iterated Function System With Variable Parameter

HUANG Xian-Tong, LIU Jian-Sheng, FU Hui

journal6, 2003, 24(2): 15-19.

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The attactors and fractal in the complex iterated function system with variable parameter were studied,and the dynamic behavior of this system was supposed.The fractal image of two-dementional n-time iterated projection was obtained by using the escape time algorithm of computer visuelization technique.The supposition was supported by the results of computer graphic experiment.

Feather-like Crystals of N-Alkyl Chitosan

DONG Yan-Ming, ZHAO Ya-Qing, WANG Hui-Wu, RUAN Yong-Hong

journal6, 2003, 24(2): 20-22.

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The N-methyl chitosan or N-ethyl chitosan was cast into films at high vacuum.Then the cast film crystallized at 25 ℃ and 65% relative humidity and the feather-like crystals appeared.The feather-like crystals were different with spherulites,which grew in the films cast at low vacuum.In addition to morphology,the birefrigence nature of feather-like crystals and spherulites was completely different.The former was negative,but the latter was positive.The feather-like crystals were believed to belong to one kind of dendritic crystals.

(∈，∈∨ｑ)-Fuzzy Normalizer and (∈，∈∨ｑ)-Fuzzy Quotient Subgroup

YAO Bing-Xue

journal6, 2003, 24(2): 23-25.

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Based on the concept of (∈，∈∨ｑ)-fuzzy subgroup introduced by S.K.Bhakat in 1992,the notions of (∈，∈∨ｑ)- fuzzy normalizer and (∈，∈∨ｑ)-fuzzy centralizer are introduced.Some properties of (∈，∈∨ｑ)-fuzzy normalizer and (∈，∈∨ｑ)- fuzzy centralizer are discussed.Then,the definition of(∈，∈∨ｑ)- fuzzy quotient group and (∈，∈∨ｑ)-fuzzy quotient subgroup is given.At last,the isomorphism theorem for (∈，∈∨ｑ)-fuzzy quotient group is established.The main results include:(1)if is a fuzzy subset of,then the (∈，∈∨ｑ)-fuzzy normalizer of is a subgroup of;(2)if is a fuzzy subgroup of,then the (∈，∈∨ｑ)-fuzzy centralizer of is a subgroup of and a normal subgroup of;(3)if and are (∈，∈∨ｑ)-fuzzy normal subgroup and (∈，∈∨ｑ)-fuzzy subgroup of,respectively,then is a (∈，∈∨ｑ)-fuzzy subgroup of.

The Calculatin of Nucleon-Nucleon Interaction Potential

WU Xiang-Yao, WANG Xin-Lin, Yin-Xin-Guo, ZHU Xiao-Mei

journal6, 2003, 24(2): 26-30.

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The equation of relative motion between two nuclei,i.e. resonance group equation,is derived from the p-s equation of six quarks system.And by resonance group method and integral transformation,the analytic representation of quark-gluon exchang potential was got.By further considering the short range part of the contribution of quark-gluon exchange potential and the intermediate-long range part of the effects of one-pion and two-pion exchange to nuclear force,the analytic representation of N-N effective potential was given,thus the nature of the nuclear force is studied all-sidedly.

Preliminary Study on Common Antigen of Tyrophagus Putrescentiae and Dermatophagoides Farine

LI Chao-Pin, CUI Yu-Bao, YANG Qing-Gui, HE Ji

journal6, 2003, 24(2): 31-34.

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Objective To investigate whether there is common antigen between Tyrophagus putrescentiae (TP) and Dermatophagoides farine (DF) or not.Methods The correlation of ELISA optic densities between TP and DF-specific IgE in atopic sera was analyzed,and TP and DF extracts were analyzed with SDS-PAGE.IgE immunoblotting and IgE inhibition immunoblotting to TP and DF extracts with atopic sera were performed also.Results The ELISA optic densities of TP and DF-specific IgE in 42 atopic sera were correlated with each other (r=0.641 5，P＜0.01).By SDS-PAGE,the protein components of the TP and DF extracts were numerous protein bands between 10 kD and 110 kD.In addition,the presence of a cross-reactive IgE binding component in the TP and DF major allergens was investigated by IgE inhibition immunoblotting experiments.Conclusion There is common antigen between Tyrophagus putrescentiae and Dermatophagoides farine.

On Fixed Point Theorems in Generating Spaces of Quasi-metric Family

XIAO Jian-Zhong, ZHU Xing-Hua

journal6, 2003, 24(2): 35-38.

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The concept of a generalized local power contractive mapping is introduced in generating spaces of quasi-metric family.The boundedness of mapping orbit and the convergence of iterative sequence are discussed.By means of these properties,some fixed point theorems for generalized local power contractive mapping are established in generating spaces of quasi-metric family.These results not only unify and extend the corresponding results of usual metric spaces and Menger probabilistic metric spaces,but also contain the fixed point theorems for contraction type mappings in Kaleva-Seikkala fuzzy metric spaces as their special cases.

The Discussion of Some Solutions of the Equation a·(t-τ)＋bｘ·(t)＋cｘ(t-τ)＋dｘ（t）＝tｋ

WU Kuo-Hua, FAN Li-Jun

journal6, 2003, 24(2): 39-42.

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By using the method of undetermined coefficients,the author discusses some solutions of the equation ａｘ·（ｔ－τ）＋ｂｘ·（ｔ）＋ｃｘ（ｔ－τ）＋ｄｘ（ｔ）＝ｔｋ.The expressions of the solutions are obtained in the following four special cases:(1)c+d≠0;(2)c+d=0,a+b-cτ≠0;(3)c+d=0,a+b-cτ=0,cτ-2a≠0;(4)c+d=0,a+b-cτ=0,cτ-2a=0.

On the 2k-th Power Mean of the Inversion of DirichletL-Function With the Weight of Gauss Sums

GAO Li, ZHAO Zhen

journal6, 2003, 24(2): 43-46.

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This paper uses estimation of the trigonomitric sums and character sums and the analytic method to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of Gauss sums.It is proved that when integer q≥2,real number Q＞1,for the arbitrary positive integers k and m,and (m,ｑ≤Ｑｑ)＝１，the power mean value formula is given as:ｑ≤Ｑ(Ａｋ（ｑ）)/(φ２（ｑ）)ｘｍｏｄ　ｑ(｜Ｇ（ｍ，ｑ）｜２)/(｜Ｌ（１，ｘ）｜２ｋ)＝（１５/π２）ｋＱ＋Ｏ（Ｑ1/2＋ε）．

Simultaneous Approximation by a New Class of Operators

WANG Li, XUE Yin-Chuan

journal6, 2003, 24(2): 47-51.

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A new class of positive linear operators is introduced,and the simultaneous approximation of unbounded functions is studied.Let ｆ∈Ｃβ[０，∞），ｒ∈Ｎ，derivative of ordern n exists in ｆ（ｘ） in [０，∞）,then ｌｉｍｎ∞Ｍ（ｒ）ｎ，α（ｆ（ｔ），ｘ）＝ｆ（ｒ）（ｘ），if ｆ（ｒ）（ｘ）∈Ｃ（ａ－η，ｂ＋η）（η＞０），then Ｍ（ｒ）ｎ，α（ｆ，ｘ）ｆ（ｒ）（ｘ） is applicable when ｘ∈[ａ，ｂ].If ｆ∈Ｃβ[０，∞），ｆ（ｘ） has derivative of order ｒ＋２ in [０，∞），then ｌｉｍｎ∞ｎ[Ｍ（ｒ）ｎ，α（ｆ，ｘ）－ｆ（ｒ）（ｘ）]＝α[ｒ（ｒ＋１）ｆ（ｒ）（ｘ）＋（２（ｒ＋１）ｘ＋ｒ）ｆ（ｒ＋１）（ｘ）＋ｘ（１＋ｘ）ｆ（ｒ＋２）（ｘ）],if ｆ（ｒ＋２）（ｘ）∈Ｃａ－η，ｂ＋η）（η＞０），then the above equation is valid in [ａ，ｂ].

Existence of Positive Periodic Solutions of Discrete Predator-Prey System With Infinite Delays

JIANG Li-Qun, MO Hong-Min

journal6, 2003, 24(2): 52-56.

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The differential model of periodic Predator-Prey with three species is studied.The existence of positive periodic solution of this system with infinite delays is discussed by using the topologic theory.It is proved that the ample conditions for the existence of positive periodic solution of this system are as follows:(ⅰ)r-1a-32-r-3a-12ｅｘｐ（2r-2ω）＞0；（ⅱ）r-1a-32-r-3a-12ｅｘｐ（2r-2ω）-r-2a-11a-32ｅｘｐ（2r-1ω）＜0；（ⅲ）-a-32a-12r-1＋a-32a-11r-2＋a-21a-12r-3＜0．

The Discussion of the Indecomposable Direct Summand of the Induced Module From θ[H]-Module

YANG Yu-Ying, HE Jiang-Chun

journal6, 2003, 24(2): 57-59.

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For absolutely indecomposable module N,T=G is the inertial group of N,G/H is the circulant group,｜G/H｜=n.F is an arbitrary domain,and f0 is a unit of F,if a∈F,and f0=an,the number of N↑G indecomposable direct summand equals the number of F[G/H] indecomposable direct summand.

Application of Electric Potential Analysis in Mensuration of Reactivity Ratios in System of VAC/DMC Copolymerization

WANG Jin-Gang, JIE Zhu-Bai, JIANG Run-Tian, ZHANG Shu-Xiang

journal6, 2003, 24(2): 60-62.

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By Cl--selective electrode,when the electropotential moves with the concentration of Cl-,proportion of PDMC in copolymerization of VAC/DMC(vinylacetic acid and methacyloyloxyethyl trimethylammonium chloride) can be determined.By this,Reactivity Ratios of VAC and DMC can be calculated as:rVAC=0.48±0.12，rDMC=3.12±0.33.This method is compared with element analysis,too.

The Two New Species of Sinocyclocheilus From Yunnan,China

LI Wei-Xian, MAO Wei-Ning, LU Zong-Min, YAN Wei-Zhu

journal6, 2003, 24(2): 63-65.

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Sinocyclocheilus wumengshanensis Li Mao et Lu.sp.nov(fig.1),holotype No.9108302,standard body length 128 mm,collected from Sanqisanluo longtan (25°30′N，103°40′E) Xundian County Yunnan on Aug.30 1991.Paratype 20 specimens No.91083030～31,91083033～34,92074014,980711001～015,collected from sanqisanluo Xundian,Deze Zhanyi and Xize Xuanwei Yunnan.D.ⅲ，7；A.ⅱ,5;P.ⅰ,16;V.ⅰ,8;C,16,Gill-rakers 5～6;L·S.67(38～42)/(22～24-v)76；pharyngeal teeth 3 row 2,3,4/4,3,2.Body depth in standard length 3.20～3.5 d 3.40,head length 3.40～4.00(3.80),length caudal peduncle 4.50～4.90(4.70),depth caudal peduncle 8.40～9.40(9.00).Snout in head 2.50～3.00(2.80) eye 3.8～7.2(5.0),interorbital 2.50～3.00(2.80).Depth of caudal peduncle 1.90～2.00(1.90) in its length.The new species is similar to S.multipunctatul (pellegrin)(1931),but differs from the latter in:(1)Barbels much longth extending from the corner of the munth to end gill opening.(2)Subunder of mouth.(3)Strong and hard last unbrached dorsal ray.(4)Distance heredity of molecule 12.6%～13.4%.Sinocyclocheilus guishanensis Li Sp.nov (fig.2),holotype No.20000929001,standard body length 106 mm,collected from Fenglongtan Guishan (24°40′N,105°45′E) Shilin County Yunnan,Spet. 29,2000.Paratype 5 specimens No.980514005～09,standard body length 68～102 mm,collected from the same locality as the holotype.D,ⅲ,7;A,ⅱ,5;P,ⅰ,13～16;V,ⅰ,8;C,ⅰ-15～16-ⅰ.Gill-rakers 5～6,lateral lin scales 73～80.Pharyngeal teeth 3 rows 2.3.4/4.3.3.Body depth in standard length 3.71～4.31(3.99),head length 3.71～4.05(3.90),length of caudal peduncle 4.25～5.43(4.66).Depth of caudal peduncle 7.80～9.64(8.56).Snout in head 2.71～3.11(2.94),eye 4.25～5.60(4.81),interorbital 3.00～3.60(3.38).Depth of caudal Peduncle 1.56～2.00(1.83).The new species distinguished from S.angustiporus Zheng et Xie(1985) by the followings given:(1)Regular of body scales.(2)Barbels much longer.(3)Distance heredity of molecule 4.4%.The type specimens are kept in Reservoir Heilongtan Shilin and Qujing Fishery Administration,Yunnan.

Source of Drug and Its Spatial Diffusion in China

SUN Feng-Hua, LIU Ji-Sheng, LI Shi-Tai

journal6, 2003, 24(2): 66-70.

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This paper sets forth the intension of drug with the viewpoints of underground economics and economic geography.It points out that unlawful production and trade of drug in China not only affects the development of personal economy,but also damages public law and order.It also points out that there are two kinds of drug production base:domestic and abroad,and the latter is the major base for China.Both historical root and present driving force are the causes of the spatial diffusion of drug in China.The social problems and hideous phenomena arise from drug diffusion make the situation of banning drug very serious.How to cut off the source of drug and control the spatial diffusion of drug is a significant strategic problem for Chinese government.

The Note Solution of Asymptote Equations for Conic Section

ZHAO Lin-Long

journal6, 2003, 24(2): 71-72.

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Conic section Γ：3ｉ，ｊ＝1aijxixj=0（aij=aji） is given.When a22=0,a12≠0,the asymptote equation is l:a21x1+a23x3=0 and l－:a11x1+ a12x2+a13x3=0

Notes on Central Limit Theorems

CHEN Dong, LAI Xiang-Rong

journal6, 2003, 24(2): 73-76.

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Several theorems associated with central limit theorems are derived,when we discussing the properties of complex random variable sequence and m-dimension real random variable sequence that keeping the central limit theorems.

Characterizations of Subinjective Modules

ZHAN Jian-Ming

journal6, 2003, 24(2): 77-78.

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This paper introduces the concept of subinjective dimension and obtains the nature of subinjective modules.Moreover subsemisimple ring,noether ring and hereditary ring are characteristiced.The main results are:(ⅰ)Any left R-module M is subinjective module if and only if SIdRM=0.(ⅱ)A ring R is subsemisimple ring if and only if SID(R)=0.(ⅲ)A ring R is Noether if and only if every subinjective module is injective.

Communication Model of Random Multiple Address System With Multiple Channels

LIANG Ping-Yuan, HUANG Guo-Sheng, LI Zu-Xin

journal6, 2003, 24(2): 79-82.

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Based on the theory of random multiple address technology,a model of the multiple channels slotted ALOHA system is proposed,and the performances are studied.Through the theoretical analysis and calculation,average successful probability,idle probability and break probability are obtained.Through the queue theory,the average waiting and abiding time in the system are obtained;at the same time,packet conflict resolution and throughput are analyzed for the system.

Simulation Study of Mobile Wireless Ad Hoc Network Based on NS2

ZHU Xi-Ping, LU Rong-Bo, WANG Xian

journal6, 2003, 24(2): 83-86.

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Ad Hoc network is a collection of mobile nodes which can be router and forwarder.At the same time it is a self-organize network with no fixed infrastructure and control center.In developing new routing protocol and designing network in Ad Hoc network,it is necessary to simulate effectively.In this paper,Ad Hoc network and NS2 is introduced at first.The method and procedure of Ad Hoc network simulation are given in NS2.In the end,AODV and DSR routing protocol is simulated in NS2.By simulation,a relevant performance parameter diagram is presented.

Extraction Methods of the Total Flavone in Bamboo Leaves

PENG Xiao-Chun, ZHOU Qing-Shan

journal6, 2003, 24(2): 87-88.

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Different factors determining the content of the total flavonids in alcohol and ester extracts has been studied in this paper.The optimum conditions was obtained by using orthogonal design.The results showed that the optimal conditions for the extraction was 70 ℃,15∶1 of 75% ethyl alcohol solution to bamboo leaves weight ratio,and extraction for 5 hours.

Program of Raising Goats by Planting Grass to Make People Rich and the Development Patter of Meat Goat Production in Xiangxi Autonomous Prefecture (Ⅰ)

ZHANG You-Xiang, LIU Zhi-Xiao, TAO Shuang-Lun, LI Jun-Nian, WANG Qing-Lin, CHEN Jun, YAO Ben-Dao, XIANG Xian-Li, QI Guang-Huai, YANG Chong-Liang

journal6, 2003, 24(2): 89-92.

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The basis in market,technology,and production as well as the good mass conciousness and leading organization lay a solid foundation for the program of making people rich through raising goat by planting Grass and the meat goat production.Not only were there some predominance in natural resources and national policy,but also in markets,geographical position and natural environment in Xiangxi autonomous prefecture.However,any factors which restrict the development of meat goat industrial in Xiangxi autonomous prefecture should not be neglected.

On the Natural Resources and Its Exploitation and Utilization in China

WANG Ju-Feng, LI Hu-Ming

journal6, 2003, 24(2): 93-96.

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The meaning and the main characteristics of natural resources are comprehensively discussed from the point of environmental science and economics.The current situation in China of soil,water,mineral,climate and biological resources is introduced.Based on the above introduction,some ideas of the exploitation and utilization of the resources are put forward by some scholars.

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