QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.     

一个来自振动理论反问题的矩阵方程

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…     

逼近严格伪压缩映象不动点的Ishikawa迭代程序

Let(X,‖·‖ ) be a Banach space.Let K be a nonempty closed,convex subset of Xand T∶K→K.Assume that T is Lipschitzian,i.e.there exists L>0 such that‖ T(x) -T(y)‖≤ L‖ x -y‖for all x,y∈K.Withoutloss of generality,assume that L≥ 1 .Assume also that T is strictly pseudocontractive.According to[1 ] this may be statedas:there exists k∈ (0 ,1 ) such that‖ x -y‖≤‖ x -y + r[(I -T -k I) x -(I -T -k I) y]‖for all r>0 and all x,y∈ K.Throughout,let N denote the set of positive in…     

二阶Volterra系统对平稳正态激励的统计响应的表示定理的数学证明

1974年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理.1984年,Naess对此定理又给出了一个数学证明.经过研究后发现,他们对定理条件的叙述都是模糊的,而且其数学证明都是有问题的.本文重新讨论了这个表示定理,给出了明确的定理条件及严格的数学证明,为它的广泛应用奠定了理论基础.     

全硅FER沸石上有机吸附物脱附行为的研究

运用热分析技术,研究吸附在体相和表面结构完美的单晶状疏水全硅FER沸石孔道中的有机化合物的脱附行为,测定亲和性指数AT值和负载量。所研究的吸附质为直链烷烃、直链烷基醇、直链烷基胺等,结果显示醇有较低的AT值,而直链烷烃有较高的AT值,胺类有最高的AT值。证明全硅FER沸石骨架对烷基、胺基呈现出强的"亲和性",而对羟基呈现出“憎性”。同时还发现吸附质的链长对脱附性质、AT值也有较大影响。     

混合溶剂中性载体镁离子选择性微电极的研究

用氯化石腊和邻硝基苯辛醚为混合溶剂制备中性载体ETH5214的镁离子选择性微电极,相对于钾离子的电位选择性系数较单独以邻硝基苯辛醚为溶剂的ETH5214镁微电极改善0.9个数量级。在纯MgCl~2和在含细胞内典型离子背景的MgCl~2溶液中,响应斜率为Nernst响应,检测下限分别为4×10^-^7mol.dm^-^3和2×10^-^5mol.dm^-^3。在pH3.5-9.5范围内,氢离子对电极的电位响应无影响。测量的重现性良好。电极的实用响应时间(t~9~5)≤3s,有效寿命长于5天。     

Ferric chloride-promoted direct trifluoromethylselenolation of nitrogen-containing heterocyclic compounds by Se-(trifluoromethyl) 4-methylbenzenesulfonoselenoate in water

The ferric chloride-promoted direct trifluoromethylselenolation of indoles and other nitrogen-containing heterocyclic compounds in water was performed by employing TsSeCF₃ as a trifluoromethylselenolation reagent. The shelf-stable and readily accessible reagents, along with the environmentally friendly and mild reaction conditions make this method an effective alternative for the trifluoromethylselenolation of electron-rich aromatics.     

Supercritical and subcritical buckling bifurcations for a compressible hyperelastic slab subjected to compression

We study the buckling bifurcation of a compressible hyperelastic slab under compression with sliding–sliding end conditions. The combined series-asymptotic expansions method is used to derive the simplified model equations. Linear bifurcation analysis yields the critical stress value of buckling, which gives a non-linear correction to the classical Euler buckling formula. The correction is due to the geometrical non-linearities coupled with the material non-linearities. Then through non-linear bifurcation analysis, the approximate analytical solutions for the post-buckling deformations are obtained. The amplitude of buckling is expressed explicitly in terms of the aspect ratio, the incremental dimensionless engineering stress, the mode of buckling and the material constants. Most importantly, we find that both supercritical and subcritical buckling could occur for compressible materials. The bifurcation type depends on the material constants, the geometry of the slab and the mode numbers.     

Comments on stabilizing layered manganese oxide electrodes for Li batteries

An electrochemical study of structurally-integrated xLi₂MnO₃•(1 −x)LiMn_0.5Ni_0.5O₂ ‘composite’ materials has been undertaken to investigate the stability of electrochemically-activated electrodes at the Li₂MnO₃-rich end of the Li₂MnO₃–LiMn_0.5Ni_0.5O₂ tie-line, i.e., for 0.7 ≤ x ≤ 0.95. Excellent performance was observed for x = 0.7 in lithium half-cells; comparable to activated electrodes that have significantly lower values of x and are traditionally the preferred materials of choice. Electrodes with higher manganese content (x ≥ 0.8) showed significantly reduced performance. Implications for stabilizing low-cost, manganese-rich, layered lithium-metal-oxide electrode materials are discussed.     

On a new FeOF polymorph: Synthesis and stability

A new polymorph of FeOF (up to now only known in its rutile type structure) was prepared by using a new synthesis approach formally based on anionic exchange using the well-known layered FeOCl as precursor. The synthesis was achieved using [CH₃C(CH₂O–)₂(COO–)B] to vehicle fluorine through the formation of soluble (CH₃)₄N⁺ [CH₃C(CH₂O–)₂(COO–)BF]⁻ and using N,N-dimethylformamide (DMF) as the reacting medium. The XRD pattern of layered FeOF can be indexed with an orthorhombic cell which doubles along the b axis (which is the direction perpendicular to the layers) with respect to that of pristine FeOCl (a = 3.792(1) Å, b = 12.699(1) Å, c = 3.321(1) Å). Both thermal analysis and diffraction indicate similar stability for the layered and rutile polymorphs. Such findings are rationalized through Density Functional Theory calculations. It is found that the energy difference between the more stable rutile and layered polymorphs is practically nul. The origin of the similar stability lies in the fact that although the number of Fe–F and Fe–O bonds is different in the two structures, the strength of both the total number of Fe–O as well as Fe–F bonds are found to be almost identical. Even if the crystal and electronic structures are considerably different, the total bonding and thus, the stability of the two polymorphs, is comparable. The stability of different FeOF rutile type structures is also analyzed.