On a generalized taylor theorem: A rational proof of the validity of the homotopy analysis method

IntroductionIn 1 7thcenturyIsaacNewton[1]gavesuchabinomialexpressionforfractionalandnegativeexponents(1 +t) α,i.e.,(1 +t) α =1 + +∞k=1α(α-1 ) (α-2 )… (α -k+ 1 )k !tk　　 (α≠ 0 ,1 ,2 ,… ) ,(1 )whoseconvergenceradiusisone.Furthermore ,theclassicalTaylorseries (seeRef.[2 ] )limm→+∞ mk=0f(k) (z0 )k !(z-z0 ) k (2 )ofacomplexfunctionf(z)atz=z0 isvalidmostlyinarestrictedconvergenceregion｜z-z0 ｜相似文献   

亚半正定阵左右逆特征值问题的进一步研究

１　引　言文［１］研究了亚半正定阵的左右逆特征值问题,它的更一般提法是问题Ｉ给定Ｘ、Ｚ使得其中Ｒｎ×ｍ表示全体ｎ×ｍ实阵的集合;即表示全体亚半正定阵集合［２］．文［１］得到了问题１有解的充要条件及解的通式,但从文［１］中主要定理给出的通式来看,子矩阵Ａ１３、Ａ１４及Ａ４３的表达式还没有得到,因此有必要对问题Ⅰ的通解作进一步的研究．本文将通过建立一个亚半正定阵的判定准则,圆满地解决以上问题． 为方便起见,本文用 及Ⅰ分别表示Ｒｎ×ｍ中秩为ｒ的矩阵集合、ｎ×正交矩阵集合及单位矩阵;而用　分别表示ｎ ×…     

A novel hydrogen‐bonded microporous framework constructed from two different metal complexes

A hydrogen‐bonded coordination supramol­ecule, (meso‐5,7,­7,­12,14,14‐hexa­methyl‐1,4,8,11‐tetra­aza­cyclo­tetra­decane‐κ⁴N)­nickel(II) [N,N‐o‐phenylenebis­(oxamato)­‐κ⁴O,N,N′,O′]nickelate(II) dihydrate, [Ni(C₁₆H₃₆N₄)][Ni(C₁₀H₄N₂O₆)]·2H₂O or [Ni(meso‐cth)]­[Ni(opba)]·2H₂O, has been prepared and characterized by X‐ray crystallographic analysis. The two complex ions, i.e. [Ni(meso‐cth)]²⁺ and [Ni(opba)]^2?, are hydrogen bonded to each other, resulting in two‐dimensional neutral supramolecular sheets. The sheets stack along the a direction to produce a three‐dimensional architecture with one‐dimensional channels in which hydrogen‐bonded chains of water mol­ecules are included.     

catena‐Poly[[[pyridinecopper(II)]bis[μ3‐4‐(2‐oxidobenzylideneamino)benzoato]] dimethylformamide disolvate], a polymer composed of dimeric dicopper building units

The title compound, {[Cu(C₁₄H₉NO₃)(C₅H₅N)]·C₃H₇NO}_n or {[Cu₂L₂(py)₂]·2DMF}_n [py is pyridine, L is 4‐(salicylideneamino)benzoate and DMF is dimethylformamide], is composed of dimeric dicopper [CuL(py)]₂ building units, which are interlinked into a one‐dimensional chain through the formation of Cu—O_COO bonds. The dimeric unit is centrosymmetric, containing two Cu^II atoms linked by bridging phenolate O atoms into a Cu₂O₂ plane with a chelating Cu—O bond length of 1.927 (2) Å and a bridging Cu—O bond length of 2.440 (2) Å. Interchain C—H...O and π–π stacking interactions are responsible for an extensive three‐dimensional structure in which the resulting channels are filled by DMF solvent molecules.     

Local Hopf bifurcation and global existence of periodic solutions in TCP system

This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu （Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350（12）, 4799-4838 （1998））.     

Structure and Magnetic Properties of a Novel Two‐Dimensional Complex from 1, 3, 5‐Benzenetricarboxylate and Neodymium(III) — {[Nd(1, 3, 5‐benzenetricarboxylate)(H2O)4] · H2O}n

A unique neodymium(III) complex, {[Nd(BTC)(H₂O)₄] · H₂O}_n (BTC = 1, 3, 5‐benzenetricarboxylate), was obtained from the reaction between Nd(ClO₄)₃ · xH₂O and Na₃BTC. Coordination bonds, hydrogen bonds, and π‐π stacking form a supramolecular structure with a novel, two‐dimensional framework. The temperature‐dependent magnetic susceptibilities were analyzed by the Curie‐Weiss law; the following values were found C = 1.32, θ = —18.3 K, respectively.     

三嗪类化合物溶解度参数及毒性构—效关系

测定了１２种三嗪类化合物的水溶解度，辛醇水分配系数和对发光菌的毒性，并用分子连结性指数建立了预测三嗪类化合物的溶解度，辛醇水分配系数及对发光菌毒性的定量结构活性相关方程，其中１０种化合物献中未见报道。e     

New Ni(II)Cu(II)Ni(II) trinuclear complexes with an 5=3/2 high-spin ground

Four new heterotrinuclear complexes have been synthesized and characterized, namely {[Ni(L)₂]₂[Cu(opba)]}(ClO₄)₂, where opba denotes o-phenylenebis(oxamato) and L stands for 1,10-phenanthroline(phen) (1), 5-nitro-l,10-phenanthroline(NO₂-phen) (2), 2,2′-bipyridyl(bpy) (S) and 4,4′-dimethyl-2,2′-bipyridyl(Me₂bpy) (4). The temperature dependence of the magnetic susceptibility of {[Ni(phen)₂]₂[Cu(opba)]}(ClO₄)₂3H₂O has been studied in the 4–300 K range, giving the exchange integral J—109 cm^?1. The HMT vs. T plot exhibits a minimum at about 100 K, characteristic of this kind of coupled polymetallic complex with an irregular spin-state structure.     

新的滇桂艾纳香寡糖BROS结构分析

以滇桂艾纳香枝叶为原料,经陶瓷膜、有机膜分离,醇沉、Sevag法除蛋白,DEAE-纤维素柱层析和SephadexG- 10,SephadexG-50凝胶柱色谱纯化得到的BROS;经HPGPC检测分析表明,BROS为均一寡糖,MALDI-TOF-MS测定分子量为1314.用IR,HPLC,甲基化分析,GC-MS,NMR (1H NMR,13C NMR,1H)HCOSY,HMQC和HMBC)等方法对BROS结构进行表征,结果表明,该寡糖由1个葡萄糖(α-D-Glcp)和7个果糖(β-D-Fru组成,残基间以→2)Fruf-(1→链接,分子末端链接为a-Glcp-(1→,→2)-β-D-Fruf推出BROS的结构式为:β-D-Fruf1-(2→1)-β-D-Fruf2-(2→1)-β-D-Fruf3-(2→ 1)-β-D-Fruf4-(2→1)-β -D-Fruf5-(2→1)-β-D-Fruf6-(2→ 1)-β-D-Fruf7-(2→ 1)-a-D-Glcp.