AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

A New Alpha-function for the Peng-Robinson Equation of State： Application to Natural Gas

Cubic equations of state(EOSs) are simple and easy at calculation. One way of improving the accuracy of a cubic EOS is through the modification of temperature-dependent energy parameter by using alpha-function.The industrial applications of natural gas are very wide and as a result, prediction of thermodynamic properties and phase behavior of natural gas is an important part of design for such processes. In this work we develop a newα-function for the Peng-Robinson(PR) EOS with the parameters optimized especially for natural gas components.The parameters are generalized as a linear function of acentric factor. The results are compared to the predictions from original PR EOS and other α-functions in literature. It is shown that the new α-function presents a good accuracy with the average deviation of 1.42% for natural gas components.

Comparative study of the adsorption performance of NH_(2)-functionalized metal organic frameworks with activated carbon composites for the treatment of phenolic wastewaters

To better understand the role of the-NH_(2)group in adsorption process of phenolic wastewaters,NH_(2)-functionalized MIL-53(Al)composites with activated carbon(NH_(2)-M(Al)@(B)AC)were prepared.The results showed that the-NH_(2)group could increase the mesopore volume for composites,which promotes mass transfer and full utilization of active sites,because hierarchical mesopore structure makes the adsorbent easier to enter the internal adsorption sites.Furthermore,the introduction of the-NH_(2)group can improve the adsorption capacity,decrease the activation energy,and enhance the interaction between the adsorbent and p-nitrophenol,demonstrating that the-NH_(2)group plays a crucial role in the adsorption of p-nitrophenol.The density functional theory calculation results show that the H-bond interaction between the-NH_(2)group in the adsorbent and the-NO_(2)in the p-nitrophenol(adsorption energy of -35.5 kJ·mol^(-1)),and base-acid interaction between the primary-NH_(2)group in the adsorbent and the acidic-OH group in the p-nitrophenol(adsorption energy of -27.3 kJ·mol^(-1))are predominant mechanisms for adsorption in terms of the NH_(2)-functionalized adsorbent.Both NH_(2)-functionalized M(Al)@AC and M(Al)@BAC composites exhibited higher p-nitrophenol adsorption capacity than corresponding nonfunctionalized composites.Among the composites,the NH_(2)-M(Al)@BAC had the highest p-nitrophenol adsorption capacity of 474 mg·g^(-1).

Adsorptive removal of tetracycline from water using Fe(Ⅲ)-functionalized carbonized humic acid

Humic acid(HA)was carbonized at 300,400 and 500℃ and then functionalized with 1 wt%–12 wt%Fe(Ⅲ)respectively[CHA300/400/500-Fe(Ⅲ)].Adsorption of such Fe(III)-functionalized carbonized HA as adsorbents to aqueous tetracycline(TC:25 mg·L^-1)was studied.The adsorption equilibrium time for CHA400-Fe(Ⅲ)to TC was 6 h faster and the adsorption removal efficiency(Re)was two times higher than that of HA/CHA.The adsorption Reof CHA400-Fe(Ⅲ)loaded 10%iron[CHA400-(10%)Fe(Ⅲ)]to TC could reach 99.8%at 8 h and still kept80.6%after 8 cycles.The adsorption kinetics were well fitted to the pseudo-second-order equation and the adsorption isotherms could be well delineated via Langmuir equations(R^2N 0.99),indicating that the homogeneous chemical adsorption of TC occurred on the adsorbents.The main adsorption mechanisms of TC were complexation Fe(III)and hydrophobic distribution.Electropositive and electronegative repulsion between TC and CHA400-(10%)Fe(Ⅲ)at lowly p H(2)and highly p H(8–10)respectively,leaded to the relatively low adsorption capacity and more notable influence of ion concentration.When the p H was between 4 and 8,TC mainly existed in neutral molecules(TCH2),so the influence of ion concentration was not obvious.The dynamic adsorption results showed that the CHA400-(10%)Fe(Ⅲ)could continuously treat about 2.4 L TC(27 mg·L^-1)wastewater with the effluent concentration as low as 0.068 mg·L^-1.Our study suggested a broad application prospect of a new,effective,lowcost and environment-friendly adsorbent CHA400-(10%)Fe(Ⅲ)for treatment of low-concentration TC polluted wastewater.

GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-FUNCTION INVOLVING A GENERAL CLASS OF POLYNOMIALS

The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.

一个推广的Hilbert型积分不等式

引入Γ-函数和ζ-函数,利用权函数方法和实分析技巧,建立一个推广的Hilbert型积分不等式.考虑了它的等价式,证明了它们的常数因子是最佳的,并通过取特殊的参数值,得到一些有意义的结果.

一个混合核Hilbert型积分不等式和它的应用（英文）

本文利用权函数方法和实分析技巧,引入Gamma函数和推广的Zeta函数联合刻划常数因子,得到一个混合核Hilbert型积分不等式和它的等价式,并证明它们的常数因子是最佳值.作为应用,通过选取特殊参数值获得一些有意义的结果.另一方面,改进参考文献中的一些相关结果.

统计物理中常用的级数和积分

给出了级数 ∑∞n=11n2 和 ∑∞n=11n4 的求解方法 ,给出了Boltzmann统计、Fermi-Dirac统计和Bose-Einstein统计中常用的一些积分的普遍求解方法 。

一个联系扩展Zeta函数的多参数Hilbert型积分不等式

利用权函数方法和实分析技巧,通过引入扩展的ζ-函数刻画常数因子,得到一个多参数Hilbert型积分不等式及其等价式,并讨论了其最佳值问题.

三七多糖调控蛋白激酶C-η及蛋白激酶C-ζ表达改善2型糖尿病大鼠肾功能的研究

目的探讨三七多糖干预2型糖尿病大鼠后大鼠肾脏病理学、肾功能、血糖、蛋白激酶C-η(PKC-η)及蛋白激酶C-ζ(PKC-ζ)的特点。方法 100只雄性Sprague-Dawley大鼠随机分为空白对照组,模型组及三七多糖低、中、高剂量组,每组20只。模型组及三七多糖低、中、高剂量组大鼠给予高脂高糖饮食6个月建立2型糖尿病大鼠模型,模型建立成功后三七多糖低、中、高剂量组大鼠分别给予三七多糖28.5、57.0、114.0 mg·kg-1·d-1灌胃治疗,模型组大鼠给予10 m L·kg-1·d-1生理盐水灌胃,空白对照组大鼠不给予任何干预。治疗4周和8周后各组分别处死大鼠各半,苏木精-伊红(HE)染色检测肾脏病理学变化,试剂盒检测肾功能及血糖水平,半定量聚合酶链反应检测肾脏组织中PKC-ηmRNA和PKC-ζmRNA的表达。结果 HE染色可见空白对照组大鼠肾小管清晰无任何损伤,而模型组大鼠肾小管有炎症反应,但肾小球病变不明显,治疗4、8周后,三七多糖低、中、高剂量组大鼠肾小管逐步缩小,细胞趋于致密。治疗4周后,三七多糖低、中、高剂量组大鼠血尿素氮水平与模型组比较显著降低(P<0.05),治疗8周后进一步降低(P<0.05);治疗8周后三七多糖中、高剂量组大鼠血尿素氮水平与空白对照组比较差异无统计学意义(P>0.05)。治疗4、8周后,三七多糖低、中、高剂量组大鼠血肌酐、血尿酸、血糖水平与模型组和空白对照组比较显著降低(P<0.05);三七多糖低、中、高剂量组大鼠血尿素氮、血肌酐、血尿酸及血糖水平比较差异无统计学意义(P>0.05)。治疗4、8周后,三七多糖低、中、高剂量组大鼠PKC-ηmRNA和PKC-ζmRNA的表达显著低于模型组(P<0.05)。治疗4周后三七多糖高剂量组大鼠PKC-ζmRNA表达与空白对照组比较差异无统计学意义(P>0.05);治疗8周后,三七多糖高剂量组大鼠PKC-ζmRNA表达显著低于空白对照组(P<0.05)。治疗4周后,三七多糖高剂量组大鼠PKC-ηmRNA及PKC-ζmRNA表达显著低于三七多糖低剂量组(P<0.05);治疗8周后,三七多糖中、高剂量组大鼠PKC-ηmRNA表达显著低于三七多糖低剂量组(P<0.05)。结论三七多糖可调节大鼠血脂,进而改善2型糖尿病大鼠肾功能,这可能与肾脏中PKC-η和PKC-ζ表达降低有关。

封闭曲线上一类含函数核奇异积分方程的Noether定理

给出一类含函数核的奇异积分方程,通过构造辅助函数,将这类含函数核的奇异积分方程转化为相应的双周期黎曼边值问题,进而讨论双周期黎曼边值问题的可解条件、一般解,得到封闭曲线情况下奇异积分方程的求解问题,给出其一般解、可解条件和可解性Noether理论.

ζ(3)的级数公式

给出ζ(3)的计算公式ζ(3)=π~2/7[1-4 sum from n=1 to ∞ζ(2n)/(2n+1)(2n+2)2^(2n)].

G-ξ图的一种错误表示

指出了物理化学教材中有关G-ξ图的一种错误表示,并阐明了错误的原因。

一类含ζ函数核的奇异积分算子的性质及应用

给出一类含ζ函数核的奇异积分算子,利用维尔斯特拉斯ζ函数的性质讨论了这类算子的若干重要性质,并在此基础上得出了相应的含ζ函数核的奇异积分方程的Noether定理.

关于混合补数序列的均值性质

利用初等数论和解析数论方法,研究m次补数与二次补数的混合均值问题,给出当m为偶数和奇数时的两个渐近公式.

SeH_n/SeH_n^-(n=1～5)的结构、热化学及电子亲合能研究

选用7种不同的密度泛函理论(DFT)方法:B3LYP,BLYP,BHLYP,BP86,B3P86,BPW91,B3PW91,采用全电子的双ζ加极化加弥散函数基组(DZP++),对SeHn/SeHn-(n=1~5)的分子结构、电子亲合能和第一离解能进行了研究.结果表明,SeH/SeH-,SeH2/SeH2-,SeH3/SeH3-,SeH4/SeH4-和SeH5/SeH5-的基态结构分别为C∝v/C∝v,C2v(1A1)/Cs(2A′),Cs(2A1)/C2v(1A1),C2v(1A1)/C4v(2A1),C4v(2A1)/C4v(1A1),其中,B3P86和B3PW91在预测分子结构方面比较好;在电子亲合能方面,BLYP方法预测是最可靠的;BP86方法预测的谐振频率与实验值接近;BHLYP能很好的预测第一离解能.

关于Riemann—ξ函数sum from n=1 to ∞ 1/n^z的注记

本文给出Riemann—ξ函数sum from n=1 to ∞(1/n^z)求和的一种行之有效的简单方法,并推导出与有关文献中的某些不同的结论。

ζ(2m)的一个递推关系式

给出了ζ（２ｍ）的一个递推关系式ζ（２ｍ）＝（－１）ｍ－１ｍπ２ｍ（２ｍ＋１）！＋ｍ－１ｋ＝１（－１）ｋ－１ζ（２ｍ－２ｋ）π２ｋ（２ｋ＋１）！（１）其中ｍ。

Allelic Variation at the TaZds-A1 Locus on Wheat Chromosome 2A and Development of a Functional Marker in Common Wheat

ζ （zeta）-carotene desaturase （ZDS） is a key enzyme for carotenoid biosynthesis, demonstrating high association with the yellow pigment （YP） content in wheat grain. Cloning ZDS gene and developing functional markers are important for marker-assisted selection in wheat breeding. In the present study, the full-length DNA sequence of a ZDS gene on wheat chromosome 2A, designated TaZds-A1, was cloned, with 14 exons and 13 introns, and it has an open reading frame （ORF） of 1 707 bp, encoding 568 amino acid residues. A co-dominant functional marker, YP2A-1, was designed based on the polymorphisms of two alleles at the locus, TaZds-Ala and TaZds-Alb, yielding 183- and 179-bp fragments in TaZds-Ala and TaZds-Alb genotypes, respectively. A new QTL for YP content was detected on chromosome 2A, co-segregating with the functional marker YP2A-1 and TaZds-A1; it explained 11.3% of the phenotypic variance for YP content in a doubled haploid （DH） population from Zhongyou 9507/CA9632. Among 217 Chinese wheat cultivars and advanced lines, the average grain YP content of 126 cultivars with TaZds-Alb allele was 7.8% higher than that of 91 cultivars with TaZds- Ala allele.

PROXIMINAL SUBSPACES OF 2-NORMED SPACES

In 1965 Gohler introduced 2-normed spaces and since then, this topic have been intensively studied and developed. We shall introduce the notion of 1-type proximinal subspaces of 2-normed spaces and give some results in this field.