Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind

Recently, the authors introduced some generalizations of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials (see [Q.-M. Luo, H.M. Srivastava, J. Math. Anal. Appl. 308 (2005) 290-302] and [Q.-M. Luo, Taiwanese J. Math. 10 (2006) 917-925]). The main object of this paper is to investigate an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol-Genocchi polynomials of higher order. For these generalized Apostol-Genocchi polynomials, we establish several elementary properties, provide some explicit relationships with the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function. We also deduce their special cases and applications which are shown here to lead to the corresponding results for the Genocchi and Euler polynomials of higher order. By introducing an analogue of the Stirling numbers of the second kind, that is, the so-called λ-Stirling numbers of the second kind, we derive some basic properties and formulas and consider some interesting applications to the family of the Apostol type polynomials. Furthermore, we also correct an error in a previous paper [Q.-M. Luo, H.M. Srivastava, Comput. Math. Appl. 51 (2006) 631-642] and pose two open problems on the subject of our investigation.     

Pd/MWCNTs(多壁碳纳米管)催化剂的制备及其Heck反应催化活性

以浓硝酸处理后的多壁碳纳米管(MWCNTs)为载体,通过微波辅助法简单而快速地制备了高度分散、粒径均一的Pd/MWCNTs催化剂。利用XRD、HRTEM、XPS等手段对催化剂进行了表征。考察了Pd/MWCNTs催化剂对Heck反应的催化活性,并优化了反应温度、碱的种类和用量等反应条件。结果表明,Pd/MWCNTs在Heck反应中具有良好的催化活性。     

A note of a modular equation of Ramanujan–Selberg continued fraction

The Ramanujan Journal - We show that if $$E/\mathbb {Q}$$ is an elliptic curve with a rational p-torsion for $$p=2$$ or 3, then there is a congruence relation between Ramanujan’s tau function...     

Some results for the q-Bernoulli and q-Euler polynomials

We show some results for the q-Bernoulli and q-Euler polynomials. The formulas in series of the Carlitz's q-Stirling numbers of the second kind are also considered. The q-analogues of well-known formulas are derived from these results.     

溶剂热/水热条件下空旷结构草酸锌的合成

应用水热法及溶剂热方法，选择两种模板剂1，2-丙二胺和4，5-二氮芴-9-酮连氮(L)设计合成了草酸锌空旷结构材料[Zn₂(C₂O₄)3][C₃H₁₂N₂]·H₂O (Ⅰ)和[Zn₂(C₂O₄)₃]·L·6[H₃O] (Ⅱ)，使用CHN元素分析、     

单晶金刚石边缘表面倾斜角度对同质外延生长的影响

利用微波等离子体化学气相沉积法,对单晶金刚石(100)晶面边缘进行精细切割抛光处理,形成偏离(100)晶面不同角度的倾斜面,在CH_4/H_2反应气体中进行同质外延生长,研究单晶金刚石边缘不同角度倾斜面对边缘金刚石外延生长的影响.实验结果表明,边缘倾斜面角度对边缘的单晶外延生长质量有影响,随着单晶金刚石边缘倾斜面角度的增大,边缘多晶金刚石数量先减少后增多,在倾斜角3.8°时边缘呈现完整的单晶外延生长特性.分析认为,边缘不同角度的倾斜面会改变周围电场强度和等离子体密度,导致到达衬底表面的含碳前驱物发生改变,倾斜面台阶表面的含碳前驱物浓度低于能形成层状台阶生长的临界浓度是减弱单晶金刚石生长过程中边缘效应的主要原因.     

含钒多金属氧酸盐的抑菌活性

按文献方法合成了α-Na₁₀[PW₉V₃(H₂O)₃O₃₇]·16H₂O、α-Na10[PW11V(H₂O)O₃₇]·16H₂O和[H₃O]₃[NH₄]₁₈[Mo₅₇V₆O₁₈₃(NO)₆(H₂O)₄₈]·56H₂O（分别简称α-PW₉V₃、α-PW₁₁V和Mo₅₇V₆）含V多金属氧酸盐。 采用纸片法分别测试了它们对大肠杆菌、枯草芽孢杆菌、酵母菌和黑曲霉菌的抑菌活性。 3种化合物均有不同程度的抑菌作用, 其中α-PW₁₁V的抑菌效果最好。     

金属Ni纳米线凝固行为的分子动力学模拟

采用EAM镶嵌原子作用势，通过经典的分子动力学模拟方法研究了不同冷却速度下的金属Ni纳米线的凝固行为，并给出了纳米线在凝固区域的结构演变过程.利用键对分析技术研究了在不同冷却速度下体系中的原子团簇在降温过程中的变化情况.研究表明，纳米线的凝固起始于表面原子，并且随着冷却速度的降低，Ni纳米线的微观结构从非晶态过渡到多壳螺旋结构，最终达到稳定的面心立方结构.多壳螺旋结构同时具有确定的结晶温度和长程无序、短程有序的非晶结构的特征. 关键词： 纳米线 凝固行为 分子动力学 键对分析     

H_3PO_4－i－C_3H_7OAl－H_2NCH_2CH_2NH_2－HOC

以乙二胺为模板剂，采用Ｈ_３ＰＯ_４－ｉ－Ｃ_３Ｈ_７ＯＡｌ－Ｈ_２ＮＣＨ_２ＣＨ_２ＮＨ_２－ＨＯＣＨ_２ＣＨ_２ＯＨ非水体系，首次合成了ＡｌＰＯ_４－１２分子筛。研究了反应物配比、酸碱度及磷源、铝源等水热晶化条件对产物物相的影响，用ＸＲＤ、ＩＲ、ＳＥＭ及ＴＧ－ＤＴＡ等对产物进行了表征，对非水体系生成的ＡｌＰＯ_４－１２中有机模板剂乙二胺的化学环境进行了研究，认为乙二胺在晶体中以两种环境存在：一部分与骨架作用力较弱；另一部分与骨架以较强的氢键相作用。     

On the apostol-bernoulli polynomials

In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.