一类非线性二阶三点边值问题的可解性

设f:[0,1]×R→R的连续函数.设η∈[0,1],α,β∈R且α≠1,β≠1为给定常数.在非线性项f满足某种增长条件的前提下考虑非线性二阶三点边值问题u"+f(t,u)=0,0相似文献   

关于C*-代数中Bohr不等式的一个注记

利用C*-代数到B(H)中的等距*-表示,研究C*-代数中的Bohr不等式,得到了4个推广的Bohr不等式成立的一些充分必要条件.主要结论如下:设p,q∈R+,且满足1/p+1/q=1,则(V) A,B∈S(S为有单位元的C*-代数),| A-B | 2+|(1-p)A-B | 2≤p|A|2+q| B|2成立当且仅当p≤2;设α,β,u,u∈R,p,q∈R+,则|αA+βB| 2+|uA+vB| 2≤p|A|2+q | B | 2成立当且仅当p≥α2+u2,q≥β2+v2且(p-(α2+ u2))(q-(β2+v2))≥(αβ+uv)2;设a,b∈R+,c∈C,则VA,B∈S,a|A|2+b|B|2+cA*B+cB*A≥0成立当且仅当ab≥|c | 2;设α,β∈R,x,y是正数,则(V)A,B∈S,|αA+βB| 2≤x|A|2+y|B|2成立,当且仅当x≥α2,y≥β2且(x-α2)(y-β2)≥α2β2.     

具有有限时滞的差分系统的稳定性

考虑具有有限时滞的差分系统 :x(n +1) =f (n,xn) ,n∈ Z,(1)其中 f :Z× Cd → Rk ,f(n,0 )≡ 0 ,n∈ Z,Cd 是所有函数φ:Z[- l,0 ]→ Rk,Z[- l,0 ] ={ - l,… ,- 1,0 }构成的集合 ,xn 定义为 xn(m) =x(n +m) ,m∈ Z[- l,0 ] .对向前差分算子得到了系统 (1)的零解的一致渐进稳定性 .     

关于C~*-代数中Bohr不等式的一个注记（英文）

利用C*-代数到B(H)中的等距*-表示,研究C*-代数中的Bohr不等式,得到了4个推广的Bohr不等式成立的一些充分必要条件1.主要结论如下:设p,q∈R~+,且满足1/p+1/q=1,则A,B∈S(S为有单位元的C*-代数),|A-B|~2+|(1-p)A-B|~2≤p|A|~2+q|B|~2成立当且仅当p≤2;设α,β,u,v∈R,p,q∈R~+,则|αA+βB|~2+|uA+vB|~2≤p|A|~2+q|B|~2成立当且仅当p≥α~2+u~2,q≥β~2+v~2且(p-(α~2+u~2))(q-(β~2+v~2))≥(αβ+uv)~2;设a,b∈R~+,c∈C,则A,B∈S,a|A|~2+b|B|~2+cA*B+cB*A≥0成立当且仅当ab≥|c|2;设α,β∈R,x,y是正数,则A,B∈S,|αA+βB|~2≤x|A|~2+y|B|~2成立,当且仅当x≥α~2,y≥β~2且(x-α~2)(y-β)≥α~2β~2.     

一类二阶常微分方程泛函边值问题解的存在性

运用打靶法考虑了二阶常微分方程泛函边值问题{x″（t）=f（t,x（t）,x′（t））,t∈[0,1],x（0）=0,x（1）=∫0^1α（t）x（t）dt解的存在性,给出了此类问题解的存在性判据,其中f：[0,1]×R^2→R满足Carathéodory条件,α∈C（[0,1],[0,∞））,且∫0^1α（t）tdt〈1.     

一类二阶常微分方程多点边值问题解的存在性

设 f :[0 ,1 ]× R2→ R满足 Carathéodory条件 ,应用打靶法考虑了二阶常微分方程多点边值问题x"=f (t,x,x ) ,t∈ (0 ,1 ) ,x(0 ) =0 ,x(1 ) = m- 2i=1aix(ξi) ,其中　 ai>0 ,ξi∈ (0 ,1 )　 (i =1 ,2 ,… ,m -2 ) ,0 <ξ1 <ξ2 <…ξm- 2 <1且 n- 2i=1aiξi <1 .讨论了其解存在性的判别准则     

数论函数及其方程

n∈N,著名的Euler函数φ(n)定义为不大于n且与n互素的正整数的个数.而Smaran-dache可乘函数S1(n)定义为S1(1)=1,如果n>1且p1α1p2α2…pkαk为n的标准素因数分解式,其中p1相似文献   

非线性波动方程的长时间解

主要讨论非线性波动方程u_(?)-△u=f(t,x,u) (*)的小初值问题的几乎整体解(almost global solution)的存在问题,证明了,若|f(t,x,u)|≤C|u|~p,x∈ R~(?),14);10存在,当初值 u(0,x),u_(?)(0,x)的范数‖u(0)‖(?)(R~(?))+‖u_(?)‖(?)(R~(?))≤δ时,(*)式的 Cauchy 问题的小振幅解在 C~1(0,T;H~1)∩ C(0,T;H~2)中唯一存在.     

一类拟线性波动方程整体解的存在性与渐近性

研究初边值问题得到了该问题{uu-△u-△ut-n∑i=1(e)/(e)xiβ(utxi) f(ut)=g(u)x∈Ω,t＞0u|(e)Ω=0t≥0u(x,0)=u0,ut(u,0)=uqx∈Ω得到了该问题整体广义解的存在性、惟一性和渐近性.     

国内外信息

钢丝中心破裂判据的试验验证钢丝拉拔过程中出现中心破裂的判据有3个。(1)艾维才(Avitzur)判据CB。CB=3sinαf(α)[(R0/Rf-1)/(R0/Rf)-2ln(R0/Rf)] 2 3[B(α)ln(R0/Rf)-(R0/Rf-1)/(R0/Rf)A(α)] (R0/Rf-1)-2(α-sinα)/sinα-mcosα[ln(R0/Rf)-(R0/Rf-1)/(R0/Rf)-1],其中R0,Rf,     

关于算术数列中三个或多个素数的和

作为圆法的一个应用,考虑算术数列中的素变数方程P1＋P2＋…＋Pk=N,Pi≡gi（modh）,j=1,2,…,k,∑1≤j≤kgj≡N（modh）,k≥3,给出了方程在大模情况下解的个数的渐近公式,即设≥3,H=sup{β：L（β＋iγ,x）=0},ε〉0,1≤h≤N^δ,0〈δ〈1,则∑p1＋p2＋…＋pk=N/pj≤N,pj≡gj（modu）,1≤j≤k（logp1）（logp2）…（loghk）=1/（k-1）!Nk-1y（k,N）＋O（Nk-2＋H＋c）＋O（Nηk＋c）＋O（Nk-2＋λ＋c）,其中η3=5/9,η4=14/5和ηk=0（k≥5）,λ={β^-,若L函数存在例外零点β^-,/0,若L函数不存在例外零点,y（k,N）=h/φ（h）^k∏p×h,p×N（1＋（-1）^k＋1/（p-1）^k）∏p×h,p｜N（1＋（-1）^k/（p-1）^k-1）.     

关于双曲函数方幂之和

设shx,chx和sinβ,cosβ是双曲正、余弦函数和三角函数,用发生函数的方法得到双曲正,余弦函数方幂与等比序列乘积之和n∑k=0 dkshrkx,n∑k=0 dk chrkx和双曲正、余弦函数带有三角函数方幂n∑k=0 shrkxsinkβ,n∑k=0 shrkxcoskβ的计算公式.     

双向加细函数和双向Riesz基小波的刻划

引入双向加细函数和双向小波的概念，通过双向加细函数的正交准则，双向加细函数基于完备仿射集小波特征，建立小波的Riesz基．在指数衰减情况下，研究双向加细方程在L2稳定解的存在性，得到双向多辨分析紧支撑小波的Riesz基完整刻划．     

Gamma函数的相关函数及其q化的完全单调性

为研究Gamma函数的相关函数及其q化的完全单调性,首先利用函数的积分表达式以及单调性理论证明函数Fα(x)=ψ′(x)+α/x-1/(x+1),fα(x)=lnx-ψ(x)-α/x以及f(x)=lnx-ψ(x)+1/x~2在(0,∞)上的完全单调性;其次基于q化的性质,利用函数的级数展开、单调性理论以及归纳法讨论上述相应函数的q化的完全单调性,并利用该性质得到2个不等式.     

1-(5-溴-2-羟基苯基)乙酮苯甲酰腙的合成及晶体结构

由1-(5-溴-2-羟基苯基)乙酮和苯甲酰肼通过缩合反应,合成新的芳香酰腙化合物:1-(5-溴-2-羟基苯基)乙酮苯甲酰腙.通过X射线单晶衍射对该化合物进行晶体结构的表征.研究表明,该酰腙为单斜晶系,空间群为P2(1)/n,晶胞学数据a=0.737 61(15)nm,α=90°,b=2.827 0(6)nm,β=116.928(12)°,c=0.860 89(13)nm,γ=90°.V=1.600 5(5)nm3,Z=4,μ=2.570mm-1,Dc=1.383mg/m3,F(000)=672,R1=0.067 6[I2σ(I)],wR2=0.187 7.     

Residual alcohol influence on NAPL saturation estimates based on partitioning tracers

The influence of residual cosolvent on the partitioning tracer technique for estimating a nonaqueous phase liquid (NAPL) saturation in porous media was investigated. Batch equilibrium and column miscible displacement tests were used to evaluate the influence of residual alcohol cosolvents in the aqueous phase on partitioning and transport of alcohol tracers through sandy soil columns containing tetrachloroethylene (PCE). As the volume fraction of cosolvent alcohol (f(c)) increased ( f(c) < or = 0.1; 10 vol %), partition coefficients (K(nc)) for the alcohol tracers linearly decreased for residual cosolvent ethanol, linearly increased for residual cosolvent tert-butyl alcohol, and did not exhibit an evident change for residual cosolvent 2-propanol. These observations are consistent with measured changes in solubility (S(c)) of the alcohol tracers over the same range (f(c) < or = 0.1) of these residual cosolvent alcohols. Column miscible displacement tests using ethanol as a residual cosolvent ( f(c) < or = 0.1) exhibited earlier partitioning tracer breakthrough leading to an underestimation of NAPL saturation (S(n)) when constant, cosolvent-free partitioning coefficients were assumed. The underestimation magnitude increased with higher initial residual cosolvent alcohol in the columns. The S(n) underestimates were not significant but were 1-10% lower than the actual S(n) (0.18). The estimated partition coefficients based on column tests with residual cosolvent (K(col)) were consistently less than those based on batch tests. Column tests with low (0.5%) and high (15%) S(n) revealed that the residual cosolvent alcohol effect was different depending on the amount of NAPL in the column. Using ethanol for a cosolvent (10%) and 2,4-dimethyl-3-pentanol as a partitioning tracer, the S(n) values were underestimated by about 17% and 5%, respectively, in the low and high NAPL saturation columns.     

Optimum Measure of Cap Color in Agaricus bisporus Wild and Cultivated Strains

Cap color was characterized on a wide range of Agaricus bisporus strains. L, a and b tristimulus coordinates were tested by linear model analysis to determine color information related to each parameter. One model was retained: log(L/(100-L)) =α* H +β. Visual cap color variation was continuous and well described by log(L/(100-L)) or H parameters. In the wild, the range of color varied from white to dark brown which would enable mushroom breeding for cap color adapted to the market.     

高效液相色谱法测定亚油酸甲酯含量

建立一种高效液相色谱测定亚油酸甲酯含量的方法。采用IntertsilO D S-SP柱,紫外检测器,检测波长为243 nm ,流动相为甲醇－水（体积比为95∶5）混合液,流速为0.8 m L/m in,进样体积为20μL,柱温为30℃。结果可知,亚油酸甲酯质量浓度和峰面积的线性回归方程是y=（2E＋06）x-43628,R 2=0.9999,线性范围是0～4.16 g/L,平均加样回收率为99.92%。     

Effect of root zone pH and form and concentration of nitrogen on accumulation of quality‐related components in green tea

Green tea quality is greatly influenced by concentrations of free amino acids, polyphenols (mainly catechins) and caffeine. The present study investigated the principal relationship between selected nutritional factors (form and concentration of N supply, root zone pH) and accumulation of these quality‐related components of tea (Camellia sinensis (L.)) plants. Tea plants were hydroponically cultured with NH , NO and NH NO at pH 4.0, 5.0 and 6.0 in one experiment and supplied with varying N concentrations (0.75, 2.0 and 4.5 mmol L^?1, NH /NO^?₃ = 3:1) in another experiment. Concentrations of free amino acids were considerably higher in NH ‐ than in NO ‐fed plants. This was attributed to the much greater absorption of NH compared with NO . Furthermore, the relative allocation of absorbed N to free amino acids, particularly theanine and glutamine, was substantially increased by NH nutrition, suggesting that NH was more readily assimilated than NO into theanine. The concentration of caffeine was increased in NH ‐ and (NH NO )‐supplied plants, whereas concentrations of catechins were reduced in (NH NO )‐fed plants. Root zone pH did not influence concentrations of most free amino acids in young shoots, with the exception of theanine, which increased at low pH (4.0) irrespective of N form; this likely stemmed from an accumulation effect, as growth decreased more strongly than N absorption. Raising the N supply increased plant N allocation to free amino acids. The increase was most striking for arginine, while theanine was only marginally affected. This may have adverse consequences for green tea quality, as less favourable taste characteristics have been attributed to arginine. Copyright © 2007 Society of Chemical Industry     

快速高分离度液相色谱-串联质谱法测定番茄酱中番茄红素的含量

本文建立了快速高分离度液相色谱-串联质谱(RRLC-MSMS)测定番茄红素的方法,通过实验优化了的分析条件。选择m/z109为定量离子,碰撞能量20V;m/z413为定性离子,碰撞能量10V。在0.02～10.0mg/L浓度范围内,曲线方程:Y=718.79x2+5964.98x-111.64,R2=0.999998。S/N=3为定性限,检出浓度0.03mg/L;S/N=10为定量限,检出浓度0.1mg/L。用1.0mg/L的溶液连续进样6次,结果的精密度RSD=3.97%。测定方法中样品前处理简单,节省溶剂,用时短,定性、定量准确,满足检测分析的要求。