Rate of stability of solutions of matrix polynomial and quadratic equations

In this paper the rate of stability of solutions of matrix polynomial equations of the typeA ₀+A ₁ X+A ₂ X ²+...+A _m X ^m =0 is studied. Particular attention is given to the case where the matrix polynomialL(λ):=A ₀+A ₁ λ+A ₂ λ ²+...+A _m λ ^m is weakly hyperbolic, i.e., for every non-zero vectorx the scalar polynomial 〈L(λ)x, x〉 has only real roots. Also the rate of stability of solutions of matrix quadratic equations of the typeXBX+XA-DX-C=0 is studied. Here the special case that is of interest to continuous-time optimal control theory, that is, the case whereB=B ^* is positive semidefinite andC=C ^*,A=?D ^*, is discussed in detail. The analogous theory for the discrete-time optimal control leads to the equation $$X = A^* XA + Q - (B^* XA)^* (R + B^* XB)^{ - 1} B^* XA,$$ and the rate of stability of solutions of this equation is also studied. Most of the problems are discussed in both real and complex settings.     

CF2自由基A态伸缩振动频率的测定

Laser induced fluorescence excitation spectroscopy has been used to determine the previously ambiguous assignments of A-state stretching frequencies of CF2 radical under supersonic free jet conditions. The measured frequencies are v’1=1012.1±0.5cm-1, v’3=1180.2±0.5cm-1, which is in good agreement with Cameron's[6] calculation result. Furthermore, some transitions attributed to the (1,n-2,0)←(0,0,0), n≦6 progressions are first reported, and new parameters are derived from the spectra obtained.     

On The Homotopy Type of

We consider the homotopy type of classifying spaces , where is a finite -group, and we study the question whether or not the mod cohomology of , as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of . This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of .

     

A Certain Functional Equation

In this paper, we use a simpler argument and solve the following more general function equation: $$\left| {f\left( {z + w} \right)} \right| + \left| {g\left( {z - w} \right)} \right| = \left| {h\left( {z + \bar w} \right)} \right| + \left| {k\left( {z - \bar w} \right)} \right|$$ where f, g, h, k are unknown entire functions and z, w are complex variables.     

Effects of ion clusters on the performance of a heavily doped erbium-doped fiber laser

A cluster model is proposed for study of the effects of the number of ions per cluster on the performance of a heavily erbium-doped fiber laser. The results indicate that both the threshold pump power and the unstable-operation region of the fiber laser increase with increasing numbers of ions per cluster.     

AlN的MOCVD生长中表面吸附的量子化学研究

利用量子化学的密度泛函理论(DFT),对AlN的MOCVD生长中表面反应前体MMAl、DMAlNH2分别在理想、NH2覆盖AlN (0001)-Al面的吸附进行研究.通过分析表面吸附位、吸附能、分波态密度图等,确定可能的稳定吸附结构和吸附倾向.研究发现:在理想和NH2覆盖的AlN(0001)-Al面,MMAl吸附在T4位和H3位,吸附概率相近,MMAl与表面形成3个Al-Al8键(理想AlN表面)或3个Al-N8键(NH2覆盖的AlN表面).在理想AlN表面,DMAlNH2吸附在Top-Top位,与表面形成N-Al8键和Al-Al8键;在NH2覆盖的AlN表面,DMAlNH2吸附在Top位,与表面形成Al-N8键.对比两种粒子在理想和NH2覆盖表面的吸附能,发现在理想表面DMAlNH2的吸附能大于MMAl,即DMAlNH2优先吸附;在NH2覆盖表面,MMAl的吸附能明显大于DMAlNH2,即MMAl优先吸附.     

硅晶体生长固液界面形貌研究

结合杰克逊界面理论、分子动力学模拟(MD)和密度泛函理论(DFT),对硅晶体(100)和(111)面生长过程中固液界面形貌进行研究,包括界面自由能变化、结构变化和生长位置吸附能等.通过杰克逊界面理论计算,发现(100)界面晶相原子和流体相原子在表面各占约50;时吉布斯自由能达到极小值,而(111)界面在表面占比约0;或100;时达到极小值,说明当热力学平衡时,(100)面趋向于粗糙面,(111)面趋向于光滑面;分子动力学模拟显示,随着生长的进行,初始光滑的固液界面在(100)面上会逐渐转变为粗糙界面,而(111)面则始终保持光滑界面生长;且在生长过程中,(100)面的生长速率明显高于(111)面,因为(100)面始终为粗糙面生长;DFT计算发现,(100)面上的所有生长位置吸附能接近,可以实现连续生长,(111)面吸附能则存在明显的差值,生长原子需要吸附在台阶处才能进行层状生长.     

Mn-mediated coupling of alkyl iodides and ketimines: a radical addition route to alpha,alpha-disubstituted alpha-aminoesters

Coupling of primary and secondary alkyl iodides with N-acylhydrazonoesters via Mn-mediated photolysis conditions affords access to tert-alkyl amines.     

Two‐dimensional hydrogen‐bonded networks in two novel glycoluril derivatives

Two new glycoluril derivatives, namely diethyl 6‐ethyl‐1,4‐dioxo‐1,2,2a,3,4,6,7,7b‐octahydro‐5H‐2,3,4a,6,7a‐pentaazacyclopenta[cd]indene‐2a,7b‐dicarboxylate, C₁₄H₂₁N₅O₆, (I), and 6‐ethyl‐2a,7b‐diphenyl‐1,2,2a,3,4,6,7,7b‐octahydro‐5H‐2,3,4a,6,7a‐pentaazacyclopenta[cd]indene‐1,4‐dione, C₂₀H₂₁N₅O₂, (II), both bearing two free syn‐urea NH groups and two ureidyl C=O groups, assemble the same one‐dimensional chains in the solid state running parallel to the [010] direction via N—H...O hydrogen bonds. Furthermore, the chains of (I) are linked together into two‐dimensional networks via C—H...O hydrogen bonds.     

Photocatalytic decolorization of methyl orange solution with potassium peroxydisulfate

Increasing environmental pollution caused by toxic dyes due to their hazardous nature is a matter of great concern. It has been generally agreed that methyl orange (MO) can be effectively degraded in aerated K₂S₂O₈ homogeneous reaction system using near-UV irradiation. In this paper photocatalytic degradation of MO solutions with K₂S₂O₈ was investigated, with particular attention on the possible underlying mechanisms. This report has shown decolorization efficiency of MO increases with the increasing of the dosage of the catalyst. There is no optimal amount of catalyst in our case, where special attention was paid on the nature of the photocatalyst itself. The current research revealed that the decolorization reaction is a pseudo first-order reaction when the concentration of MO is below 20 mg L⁻¹ and the decolorization reaction is zero-order reaction when the concentration of MO is above 100 mg L⁻¹, but the Langmuir-Hinshewood kinetic model does not describe this. The influence of IO₄⁻, BrO₃⁻ and H₂O₂ were investigated in detailed. Several observations indicate that the mechanism is not involved in hydroxyl radical attacks in MO degradation with K₂S₂O₈ by UV irradiation. The possible underlying mechanisms are direct oxidation of the MO by S₂O₈²⁻ and hydrogen attraction by SO₄^•−.