A Second Main Theorem on ℙ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> for difference operator

The main result of this article is an extension of the Second Main Theorem, of Halburd and Korhonen, for meromorphic functions of finite order. Their result replaces the counting function of the ramification divisor N _ramf(r) in the classical Second Main Theorem by the counting function of a finite difference divisor N _pair(r). In this article, the Second Main Theorem of Halburd and Korhonen is extended to the case of holomorphic maps into ℙ ⁿ of finite order.     

The Knoevenagel reaction: analysis and recycling of the ionic liquid medium

A study involving the scope of substrate in the Knoevenagel reaction in an IL medium has been conducted. Reactivity trends favor formation of the condensation product using electron deficient aryl aldehydes. Use of electron rich aldehydes and ketones lead to lower levels of conversion and no measurable amounts of condensation products, respectively. A recycling study confirmed that the reaction medium could be used multiple times affording, with each run, the desired condensation product 1a in excess of 90% conversion. Post-run analyses of the IL documented that the IL medium was unaltered upon reuse.     

基于平板振动精确化方程求解动应力集中问题

基于文献[8]给出的平板弯曲振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究.文中给出了分别基于Mindlin板与精确化板方程在不同参数下圆孔动弯矩集中系数的数值结果,并对结果进行了对比分析和讨论.结果表明:在较低频率和薄板情况下,基于文献[8]的方程与基于Mindlin板理论得到的动弯矩结果是基本一致的;在较高频率和厚板情况下,基于文献[8]的方程与基于Mindlin板理论的动弯矩结果相差较大,最大值超出可达16%.由于文献[8]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此其分析计算结果更精确一些.      

Scattered waves and motions of marine vessels advancing in a seaway

The steady forward motion of a marine vessel modifies the incident and scattered waves as well as its dynamic characteristics in a seaway. Small amplitude assumptions of the surface waves and vessel dynamic responses lead to linearization of the potential flow problem and its solution in the frequency domain. The mathematical formulation adopts a translating coordinate system at the vessel forward speed. The free surface boundary condition accounts for the modification of the uniform current around the vessel and a new radiation condition takes into account the Doppler shift of the scattered waves. A boundary element model, based on the Rankine source distribution, describes the steady and oscillatory flows around the vessel. Stokes’ theorem allows evaluation of the surface integrals involving the so-called m-terms due to oscillation of the vessel in a current. Through a numerical experiment with a Wigley hull form, we establish the convergence of the numerical model, verify the radiation condition, and examine the scattered wave patterns for a full range of forward speeds. Previous laboratory data provides validation of the computed hydrodynamic coefficients and dynamic response as well as the potential flow model for general seakeeping applications.     

Sensor placement method for dynamic response reconstruction

Structural dynamic response reconstruction can be conducted by transforming the measured responses into responses at other selected locations of a structure. The quality of the reconstructed responses strongly depends on the quality of the measured response data, which further depends on the number and location of sensors in the structure. A new sensor placement method is proposed in this paper for better prediction of the dynamic response reconstruction.     

Divalent metal phosphonate coordination polymers constructed from a dipiperidine-based bisphosphonate ligand

The ligand 4,4'-dipiperidine-N,N'-bis(methylenephosphonic acid), H(4)L, has been reacted with divalent metal salts under solvothermal conditions to yield seven new metal phosphonate coordination polymers. The compounds have been characterized by elemental analyses and their structures determined by single-crystal X-ray diffraction. Zn(2)(L)(H(2)O)(2) and Co(2)(L)(H(2)O)(2) have (different) layered structures, while Mn(2)(L)(H(2)O)(3) has a chain motif. In these compounds, the N atoms of the ligand bind to the metal ions. α-Co(2)Cl(2)(H(2)L), formed from CoCl(2)·6H(2)O and H(4)L in ethanol, is also layered but the N atoms of the ligand are protonated. The Co atoms are tetrahedral, coordinated by three phosphonate oxygen atoms and a chloride ion. A polymorph of this compound, β-Co(2)Cl(2)(H(2)L), was obtained from a mixed ionic liquid under microwave irradiation. The primary difference between the polymorphs is the orientation of the phosphonate group relative to the dipiperidine. When reacted hydrothermally with Sn(II)C(2)O(4), H(4)L partially decomposes, producing phosphate ions which are incorporated into the structure of Sn(6)O(2)(H(2)L)(PO(4))(2)·4H(2)O. In this compound, the N atoms of the ligand are protonated, and two oxide anions are incorporated for charge balance. A second phase is obtained from the same reaction, which was determined to be Sn(7)O(L)(3). This compound has a layered structure which contains relatively large voids within the inorganic portion of the layer. These structures are discussed, as well as factors influencing the state of protonation in the final compounds. The choice of solvent and temperature were found to have a significant influence on the type of structure obtained.     

Exceptionally strong multiphoton-excited blue photoluminescence and lasing from ladder-type oligo(p-phenylene)s

We report the synthesis and investigation of multiphoton absorption properties of a novel series of diphenylamino-end-capped ladder-type oligo(p-phenylene)s which exhibit greatly enhanced and efficient multiphoton (from two- to five-photon) upconverted blue photoluminescence with which the record-high intrinsic three-photon absorption cross-section of 4.56 × 10(-76) cm(6) s(2) in the femtosecond regime has been obtained. Exceptionally efficient two- to five-photon-excited lasing in the blue region has also been demonstrated in which the highest two-photon-excited lasing efficiency of 0.34% has been achieved.