关于亚纯函数的一个唯一性定理

设f(z)和g(z)是两个非常数的亚纯函数,a(z)和b(z)(b(?)a~(k),k为非负整数)是关于f(z)和g(z)的小函数,并且6(a)=S(a,f) 6(a,g)>1,如果∞是f(z)和g(z)的CM分担值,b是f~(k)(z)和g~(k)(z)的CM分担值,则或者f~(k)(z)≡g~(k)(z)或者f~(k)(z)=(a~(k))(z)-b(z))e~(h(z)) a~(k))(z)和g~(z)=(a~(k)(z)-b(z))e~(-h(z)) a~(k)(z)成立,其中h(z)是整函数。     

亚纯函数及其线性微分多项式的唯一性

设f(z)是开平面上的亚纯函数,N(r,f)为f(z)在圆|z|≤r上极点的计数函数,m(r,f)为逼近函数.T(r,f)=m(r,f) N(r,f),T(r,f)称为f(z)的特征函数.F(z)=(fn)(z) a1(z)f(n-1)(z) … an(z)f(z)是f(z)的线性微分多项式,其中n是正整数,a1(z),a2(z),…,an(z)均是f(z)的小函数.研究f(z)和F(z)的唯一性问题.证明了:f(z)为满足N(r,f)≤1f(z)的两个相互判别的小函数,若f(z)和F(x)几乎CM分担a(z)和b(z),则f(z)≡F(z).     

分担有理函数的亚纯函数

研究亚纯函数的惟一性,证明如下结果:设p(z)和q(z)分别为n1和n2次多项式且互素, f(z)和g(z)是两个超越亚纯函数,n≥max{11,2n1 4n2 3}是一个正整数,如果f n(z)f'(z),gn(z)g'(z)分担有理函数p(z)/q(z)CM,则f(z)=c1Q(z)eα(z),g(z)=c2Q-1(z)e-α(z),这里c1,c2是两个常数,Q(z)是一个有理函数,α(z)是一个非常数多项式,满足(c1c2)n 1(Q'(z)/(Q(z) α'(z))2≡-(p(z)/q(z))2;或者f(z)≡tg(z),其中t是满足tn 1=1的常数.     

具有极点和正则点的非线性迭代方程的解析解

本文主要研究具有极点和正则点的非线性迭代方程G(z)x′(z)=x(αz+βx(z))+F(x(z))的解析解.在第二章和第三章中通过把已知方程转化为不含未知函数迭代的辅助方程[ψ(λz)-αψ(z)][λψ′(λz)-αψ′(z)]G(ψ(z))=ψ(z)[ψ(λz)-αψ(z)][ψ(λ2z)-αψ(λz)]ψ′(z)+β2ψ(z)ψ′(z)F(1/β(ψ(λz)-αψ(z))),z∈C.和G(g(z))[γg′(γz)-αg′(z)]=b(γ2z)-αg(γz)]g′(z)+βg′(z)F(1/β(g(γz)-αg(z))).从而得到原方程在极点和正则点处的解析解x(z)=1/β[ψ(λψ-1(z))-αz,x(z)=1/β[g(γg—1(z))-αz].     

一类差分方程的亚纯解与亚纯函数分担3个值的唯一性

利用亚纯函数的Nevanlinna值分布理论和分类讨论的思想方法, 研究了差分方程a1(z)f(z+1)+a0(z)f(z)=0的有穷级亚纯解f(z)与任一亚纯函数g(z)分担0, 1, CM时的唯一性问题, 得到f(z)g(z)或者f(z)g(z)1, 其中a1(z)和a0(z)是非零多项式且满足a1(z)+a0(z)0.     

分担全纯函数的亚纯函数的正规族

主要研究了亚纯函数分担全纯函数的正规族问题,证明了:如果F是区域D上的亚纯函数族,且满足L[f]=a0f′+a1f(a0≠0),a,b,c,d为D 上的4个全纯函数。如果对任意的f∈F,满足a(z)≠d(z),b(z)+a1(z)a(z)+a0(z)a′(z)≠2c(z),c(z)-a0(z)a′(z)-a1(z)a(z)≠0,f(z)=a(z) L[f](z)=b(z)且L[f](z)=c(z) f(z)=d(z),则F在D 正规。
     

一类高阶线性微分方程解的复振荡性质

研究了高阶线性微分方程f(k)+Ak-1(z)epk-1(z)f(k-1)+Ak-2(z)epk-2(z)f(k-2)+…+A0(z).ep0(z)f=0和f(k)+Ak-1(z)epk-1(z)f(k-1)+Ak-2(z)epk-2(z)f(k-2)+…+A0(z)ep0(z)f=F(z)解的增长性问题,其中pj(z)=ajzn+bj,1zn-1+…+bj,n,Aj(z)和F(z)是有限级整函数.针对pj(z)中aj(j=0,1,…,k-1)的幅角主值不全相等的情形,得到了方程解的增长级的精确估计.     

涉及微分多项式和多项式的亚纯函数正规族

k,l∈N,且k≥2,设F为D内亚纯函数族,对f∈F,在D内的零点之级≥k 1,极点之级≥2.h(z)为D内的全纯函数,在D内的零点之级≥2,且h(z)0.设a1(z),a2(z),...,ak-1(z)和b1(z),b2(z),...,bl(z)为D内的全纯函数.置H(f)(z)=f(k)(z) ak-1(z)f(k-1)(z) ... a1(z)f ′(z) b1(z)f(z) ... bl(z)f l(z).若对f∈F,有H(f)(z)≠h(z)(z∈D)成立,则F在D内正规.     

复合解析函数族分担解析函数的一正规定则(英文)

得到一个正规定则:设α(z)和F分别是区域D上的解析函数与解析函数族,P(z)是次数P不低于2的多项式.如果对族F中函数f(z)和g(z),Pf(z)和P g(z)分担α(z)IM,并且下述条件之一成立:①对任何z0∈D,P(z)-α(z0)有至少两个不同的零点;②存在z0∈D使得P(z)-α(z0)仅有一个零点β0,同时k≠lp,其中l和k分别是f(z)-β0和α(z)-α(z0)在z0处的零点重数,α(z)不是常数.那么F在D内正规.     

分担全纯函数的亚纯函数的正规族（英文）

主要研究了亚纯函数分担全纯函数的正规族问题,证明了:如果F是区域D上的亚纯函数族,且满足L[f]=a0f'+a1f(a0≠0),a,b,c,d为D上的4个全纯函数。如果对任意的f∈F,满足a(z)≠d(z),b(z)+a1(z)a(z)+a0(z)a'(z)≠2c(z),c(z)-a0(z)a'(z)-a1(z)a(z)≠0,f(z)=a(z)L[f](z)=b(z)且L[f](z)=c(z)f(z)=d(z),则F在D正规。     

四元数矩阵方程AXB+CXD=E的M自共轭解

把实数域上的M对称矩阵的概念推广到四元数体上,形成M自共轭矩阵,然后在四元数体上讨论矩阵方程AXB+CXD=E的M自共轭解及其最佳逼近问题.利用四元数矩阵的实分解和复分解,以及M自共轭矩阵的特征结构,借助Kronecker积把约束四元数矩阵方程转化为实数域上的无约束方程,克服了四元数乘法非交换运算的困难,并得到该方程具有M自共轭解的充要条件及其通解表达式.同时在解集非空的条件下,运用矩阵的分块技术及矩阵的拉直算子,获得与预先给定的四元数矩阵有极小Frobenius范数的最佳逼近解.由于M自共轭矩阵是四元数自共轭矩阵的推广,因此所得结果拓展了该方程的结构解类型.     

3种苏铁属植物总黄酮、总多糖含量及抗氧化活性研究

为探究锈毛苏铁(Cycas ferruginea)、叉孢苏铁(C.segmentifida)和石山苏铁(C.sexseminifera) 3种苏铁属(Cycas)植物的总黄酮、总多糖含量以及抗氧化活性,本研究采用超声波辅助法对其根、叶柄、叶、雄球花、茎干的总黄酮及总多糖含量进行提取,以DPPH自由基(DPPH·)、羟自由基(·OH)、超氧阴离子自由基(O^-₂·)清除率评价其抗氧化活性,并采用Pearson相关性分析法分析相关性。结果表明：锈毛苏铁、叉孢苏铁和石山苏铁叶的总黄酮含量较高,大小依次为锈毛苏铁(8.61 mg·100 mg^-1)>叉孢苏铁(7.82 mg·100 mg^-1)>石山苏铁(1.04 mg·100 mg^-1);茎干中总多糖含量最高,大小依次为叉孢苏铁(28.32 mg·100 mg^-1)>石山苏铁(24.43 mg·100 mg^-1)>锈毛苏铁(16.59 mg·100 mg^-1<...     

邻香草醛缩胱氨酸双Schiff碱的合成及其对粟酒裂殖酵母细胞生长代谢的热动力学研究

用摩尔比为2:1的邻香草醛(C_8H_8O_3)与L-胱氨酸(C_6H_(12)N_2O_4S_2)反应,合成了一种新的双Schiff碱化合物--双{2-[(3-巯基丙酸钠)-2-亚胺基-甲基]-6-甲氧基-苯酚}(OVCS)。通过元素分析、红外光谱、核磁共振等手段对其组成和结构进行了表征,确定其化学式为Na_2(C_(22)H_(22)N_2O_8S_2),采用TAM air微量热仪测定了新合成的Schiff碱化合物(OVCS)在305.15 K时对粟酒裂殖酵母细胞作用的产热曲线;根据产热曲线计算了在OVCS作用下,粟酒裂殖酵母细胞生长代谢的最大发热功率p_(max)、速率常数k、传代时间tG、抑制率I和半抑制浓度C_(I,50)等热动力学参数。通过实验可以发现随着OVCS浓度的增加,粟酒裂殖酵母细胞的生长代谢速率常数k、生长代谢的总热效应Q_(total)、最大发热功率p_(max)均减小,抑制率I、达到生长代谢最大功率所需时间t_(max)、传代时间tG均增加等规律,半抑制浓度C_(I,50)为35.99 mg/L(或9.62×10~(-2)mol/L)。实验结果表明,OVCS对粟酒裂殖酵母细胞有抑制作用,且浓度越大,抑制作用越强。     

Comparison study of chitosan/β-cyclodextrin and carboxymethyl chitosan/β-cyclodextrin microspheres

To compare two microspheres of chitosan/β-cyclodextrin and carboxymethyl chitosan/β-cyclodextrin loaded theophylline as pulmonary sustained drug delivery carriers, the characteristics and ciliotoxicity were studied. The drug loadings of chitosan/β-cyclodextrin and carboxymethyl chitosan/β-cyclodextrin microspheres were 21.09% and 21.42%, and the encapsulation efficiencies were 91.40% and 92.80%. The distributions of 50% (d _0.5) of chitosan/β-cyclodextrin and carboxymethyl chitosan/β-cyclodextrin microspheres were 4.89 and 5.83 μm, respectively. Both microspheres showed spherical shape with smooth or wrinkled surfaces. FT-IR of chitosan/β-cyclodextrin microspheres demonstrated that theophylline had formed hydrogen bonds with chitosan and β-cyclodextrin, while for the carboxymethyl chitosan/β-cyclodextrin microspheres theophylline had interaction with carboxymethyl chitosan. The moisture absorption showed that an equilibrium was reached within 24 h. The two microspheres possessed better adaptability. In vitro release of theophylline from chitosan/β-cyclodextrin microspheres was slower than that from carboxymethyl chitosan/β-cyclodextrin microspheres at pH 6.8. Biography: LI Ruobao(1968–), male, Associate professor, research direction: foundation research of respiratory system.     

Synthesis process of Ba-ferrites from α-FeOOH and γ-FeOOH and investigation of magnetic properties

The claviform BaFe₁₂O₁₉ crystals were synthesized by the precipitation-toptactic reaction method using α-FeOOH and γ-FeOOH as raw materials respectively. The synthesis processes of BaFe₁₂O₁₉, studied by XRD, SEM, EDS, FT-IR, and TG-DTA techniques, included preparations of precursor γ and precursor α, formations of α-Fe₂O₃ and BaFe₂O₄, and production of rod-like BaFe₁₂O₁₉ through dehydroxylation of pod-like FeOOH, followed by reactions of α-Fe₂O₃ with BaCO₃ and BaFe₂O₄. The crystallinity of α-Fe₂O₃ and BaCO₃ from precursor α was better than from precursor γ due to the direct dehydroxylation of α-FeOOH, resulting in a lower nucleation rate and better crystallinity of BaFe₂O₄. BaFe₁₂O₁₉ prepared from precursor α showed lower crystallinity and purity with a higher length-diameter ratio than from precursor γ. The VSM results proved that the appearance of final products had an important influence on magnetic properties.     

Functional Imaging of Breast Tissue and Clinical Application

0Introduction Near infrared(NIR)techniquesarebasedonsensitive,quantitativemeasurementsoffunctionalcontrastbe tweenhealthyanddiseasedtissue.Recently,researchersshowgreatinterestinmeasuringfunctionalpropertiesofbreasttis suesuchashemoglobinconcentrationoroxygensaturationbyNIRspectroscopyandNIRimaging[1,2].NIRlightcanpene trateseveralcentimetersintotissuebeforeitisattenuatedbe lowdetection.ThemainintrinsicmechanismsofNIRlightat tenuationintissuearethescatteringduetoindexofrefractionvariatio…     

Temperature effects on ethylene and methane production from temperate forest soils

Change in temperature affects the activity of soil microorganisms.However,there is limited knowledge about temperature effects on ethylene(C2H4) and methane(CH4) production from forest soils.Topsoil samples(0―5 cm) collected from different temperate forest stands(e.g.,Pinus sylvestris L.,Cryptomeria japonica,and Quercus serrata) were used to compare C2H4 and CH4 production from soils at temperature from 5 to 35℃ under oxic and anoxic conditions.The rates of C2H4 and CH4 production from soils under oxic cond...     

Coral reef ecosystems in the South China Sea as a source of atmospheric CO<Subscript>2</Subscript> in summer

Field measurements of air-sea CO2 exchange in three coral reef areas of the South China Sea (i.e. the Yongshu Reef atoll of the Nansha Islands, southern South China Sea (SCS); Yongxing Island of Xisha Islands, north-central SCS; and Luhuitou Fringing Reef in Sanya of Hainan Island, northern SCS) during the summers of 2008 and 2009 revealed that both air and surface seawater partial pressures of CO2 (pCO2) showed regular diurnal cycles. Minimum values occurred in the evening and maximum values in the morning. Air pCO2 in each of the three study areas showed small diurnal variations, while large diurnal variations were ob-served in seawater pCO2. The diurnal variation amplitude of seawater pCO2 was ~70 μmol mol–1 at the Yongshu Reef lagoon, 420–619 μmol mol–1 on the Yongxing Island reef flat, and 264–579 μmol mol–1 on the reef flat of the Luhuitou Fringing Reef, and 324–492 μmol mol–1 in an adjacent area just outside of this fringing reef. With respect to spatial relations, there were large differences in air-sea CO2 flux across the South China Sea (e.g. ~0.4 mmol CO2 m–2 d–1 at Yongshu Reef, ~4.7 mmol CO2 m–2 d–1 at Yongxing Island, and ~9.8 mmol CO2 m–2 d–1 at Luhuitou Fringing Reef). However, these positive values suggest that coral reef ecosystems of the SCS may be a net source of CO2 to the atmosphere. Additional analyses indicated that diurnal variations of surface seawater pCO2 in the shallow water reef flat are controlled mainly by biological metabolic processes, while those of deeper water lagoons and outer reef areas are regulated by both biological metabolism and hydrodynamic factors. Unlike the open ocean, inorganic metabolism plays a significant role in influencing seawater pCO2 variations in coral reef ecosystems.     

三种速生人工林凋落物的持水性能

在广西国营高峰林场界牌分场选择立地条件、营林和管理措施、林分长势基本一致的5年生尾巨桉无性系3229(Eucalyptus3229)、厚荚相思(Acaciac rassicarpa)和马占相思(Acacia mangium)速生人工林,采集林下凋落物测定单位面积储量、持水量、持水率和持水速率,研究3种速生树种人工林下凋落物的持水性能。结果表明,厚荚相思凋落物的持水量和持水率最大,分别达18.40×103kg.hm-2和70%,尾巨桉3229的次之,分别为17.34×103kg.hm-2和50%,马占相思的最小,分别是13.49×103kg.hm-2和45%。厚荚相思和尾巨桉无性系3229的持水性能比马占相思的强。     

Theoretical study of partial oxidation of ethylene by vanadium trioxide cluster cation

Density functional theory （DFT） study of reaction between vanadium trioxide cluster cation （VO3^＋） and ethylene （C2H4） to yield VO2^＋ ＋ CH3CHO （acetaldehyde） and VO2CH2^＋ ＋ HCHO （formaldehyde） is carried out. Structures of all reactants, products, intermediates, and transition state in the reaction have been optimized and characterized. The results show unexpected barriers in the reaction due to the existence of a η^2-O2 moiety in the ground state structure of VO3^＋. The initial reaction steps combining ethylene adsorption, C=C activation and O-O cleavage are proposed as rate limiting processes. Comparison of reactions of VO3^＋ ＋ C2H4 with VO3 ＋ C2H4 and VO2^＋ ＋ C2H4 in the previous studies is made in detail. The results of this work may shed light on the understanding of C=C bond cleavage in related heterogeneous catalysis.