对一道椭圆中两条直线斜率乘积为定值试题的探究

先给出一道广东省2021届高三综合能力测试题的证法,然后将试题的条件一般化,探究得到椭圆的一组性质,类比得到抛物线中的相关性质.     

敬告读者——《光谱学与光谱分析》已全文上网

从2008年第7期开始在《光谱学与光谱分析》网站(www.gpxygpfx.com)“在线期刊”栏内发布《光谱学与光谱分析》期刊全文,读者可方便地免费下载摘要和PDF全文,欢迎浏览、检索本刊当期的全部内容;并陆续刊出自2004年以后出版的各期摘要和PDF全文内容。2009年起《光谱学与光谱分析》每期出版日期改为每月1日。     

含硫氨基酸与本征及缺陷石墨烯表面的相互作用

半胱氨酸及蛋氨酸是人体的两种含硫氨基酸,在生物活性中发挥着巨大的作用.本研究采用密度泛函理论方法对以上两种氨基酸在本征及缺陷石墨烯表面的吸附机理进行了详细研究.主要考虑了两种吸附体系:半胱氨酸及蛋氨酸平躺在两种石墨烯表面;两种氨基酸垂直地放置于两种石墨烯表面,且含硫的基团靠近表面.研究结果表明,半胱氨酸及蛋氨酸初始构型对它们之间的相互作用有一定的影响.两种氨基酸平躺时有较大的吸附能.此外,吸附能的结果显示两种氨基酸可以更好的与缺陷石墨烯表面紧密结合.同时,蛋氨酸与本征及缺陷石墨烯相互作用均大于半胱氨酸与本征及缺陷石墨烯相互作用.模拟结果有望为含硫氨基酸的石墨烯传感器提供有用的指导.     

Mass and isotopic concentrations of water-insoluble refractory carbon in total suspended particulates at Mt.Waliguan Observatory(China)

Mass concentration and isotopic values δ¹³C and ¹⁴C are presented for the water-insoluble refractory carbon（WIRC） component of total suspended particulates（TSP）,collected weekly during 2003,as well as from October 2005 to May 2006 at the WMO-GAW Mt.Waliguan（WLG） site.The overall average WIRC mass concentration was（1183±120）ng/m³（n = 79）,while seasonal averages were 2081 ±1707（spring）,454±205（summer）,650±411（autumn）,and 1019±703（winter） ng/m3.Seasonal variations in WIRC mass concentrations were consistent with black carbon measurements from an aethalometer,although WIRC concentrations were typically higher,especially in winter and spring.The δ¹³C PDB value（-25.3 ± 0.8）%.determined for WIRC suggests that its sources are C₃ biomass or fossil fuel combustion.No seasonal change in δ¹³C PDB was evident.The average percent Modern Carbon（pMC） for ¹⁴C in WIRC for winter and spring was（67.2 ± 7.7）%（n = 29）.Lower pMC values were associated with air masses transported from the area east of WLG,while higher pMC values were associated with air masses from the Tibetan Plateau,southwest of WLG.Elevated pMC values with abnormally high mass concentrations of TSP and WIRC were measured during a dust storm event.     

Isolation and Crystal Structure of Ent-kaurane Diterpenes from Rubus corchorifolius L. f.

In this study, ent-Kaurane-3β,16β,17-triol(1) and ent-kaurane-2α,16β,17-triol(2), were isolated from the leaves of Rubus corchorifolius L. f. Their structures were elucidated based on extensive spectroscopic analysis. NMR experiments identified the two compounds and X-ray crystallographic analysis confirmed their crystal structures. The crystal of 1 belongs to monoclinic with space group P21 and a = 10.7641(3), b = 7.2789(3), c = 11.7862(4) , β = 95.275(3)°, V = 919.55(6) 3, Z = 2, C20H34O4, Mr = 322.49 g/mol, Dc = 1.230 g/m3, F(000) = 376, λ = 1.54178 , μ = 0.661 mm-1, R = 0.0319, and wR = 0.0811 for 10889 observed reflections(Ⅰ 2σ(Ⅰ)). The crystal of 2 is classified as orthorhombic with space group P212121 and a = 10.7641(3), b = 12.72224(19), c = 21.3929(3) , V = 1748.94(4) 3, Z = 4, C20H34O4, Mr = 322.47, Dc = 1.225 Mg/m3 F(000) = 712, λ = 1.54184 , μ = 0.625 mm-1, R = 0.0303 and w R = 0.0759 for 10470 observed reflections(Ⅰ 2σ(Ⅰ)). Meanwhile, the compound revealed low inhibitory activities toward Hep G2, MCF-7, and SCG-7901 cells.     

Stereoselective interactions of chiral dipeptides on amylose based chiral stationary phases

Dipeptides are stereo-specifically involved in several biological functions that are challenging to separate enantiomerically. Elution order of enantiomers is an important issue in chiral chromatography. Amylose tris-(3,5-dimethylphenylcarbamate) chiral stationary phase(CSP) is the best and most-widely-used CSP in chiral separations, but experimental data of enantiomeric separation of dipeptides on this CSP is lacking. Simulation studies were conducted to determine the order of elution and the chiral recognition mechanism of didpetides on this CSP. Results indicated that the docking energy of SR-enantiomers were higher than SS-antipodes. The range of docking energies for SR-enantiomers was -7.44 to -5.92 kcal/mol with CSP, but -7.15 to -5.87 kcal/mol for SS-stereoisomers. Therefore it is predicted that SS-enantiomer will elute first, followed by SR-antipode. Furthermore, hydrogen bondings, van der Waal’s interactions and electrostatic interactions were observed among SR- and SSenantiomers and chiral grooves of CSP. The number of hydrogen bonds was one in each enantiomer binding except S-Ala-R-Tyr, which contained two hydrogen bonds. No hydrogen bond was found in S-Ala-R-Trp, S-Leu-S-Trp, and S-Leu-S-Tyr dipeptides bindings. The chiral recognition mechanisms dictate different strengths of stereoselective bindings of the enantiomers on CSP.     

广义线性多乘积问题的完全多项式时间近似算法

本文针对广义线性多乘积极小化问题,通过一系列的线性规划问题的解提出一种求其全局最优解的完全多项式时间近似算法,并给出该算法的计算复杂性,且数值算例验证该算法是可行的.     

两类图的(d,1)-全标号

主要讨论了W_n与C_m的笛卡尔积和均衡完全r-部图K_r(n)的(d,1)-全标号,并得出了(d,1)-全数λ_d~T(W_n□C_m)和λ_d~T(K_(r(n)))的确切值.     

α-混合序列部分和乘积精确渐近性的一般形式

利用前人获得的α-混合序列部分和乘积的渐近分布的结果,对一般的边界函数和拟权函数得到了α-混合序列部分和乘积的精确渐近性的一般形式.