在探究过程中提升核心素养——以高中教材中的一道习题为例

笔者以人民教育出版社普通高中数学教材"拓广探索"栏目中的一个结论开放型题目为例,在比较、分析、思考的过程中认清题目的特征,利用类比的思维方法深入探究题目的本质,在体会数学美、发现数学美、欣赏数学美的过程中探究题目;在发现问题、提出问题、解决问题的过程中发展学生的创新意识;在数学抽象、逻辑推理、数学建模的过程中提升学生的核心素养,展示题目的探究过程,给出题目的探究结果,提高学生的实践能力.     

Supramolecular Terbium-SIP Complex Pillared by 4,4'-Bipyridyl,{[Tb(SIP)(H_2O)_5]_2(bpy)_3(H_2O)}n:Synthesis,Crystal Structure and Photoluminescence

The supramolecular terbium complex, {[Tb(SIP)(H2O)5]2(bpy)3(H2O)}n (NaH2SIP= 5-sulfoisophthalic acid monosodium salt and bpy=4,4'-bipyridyl), has been synthesized by the hydrothermal reaction of Tb4O7 with NaH2SIP and bpy at 165 ℃, and characterized by single-crystal X-ray diffraction, elemental analysis, IR spectrum, powder X-ray diffraction and photoluminescence spectrum. It crystallizes in a monoclinic system, space group C2/c, with a= 30.6840(1), b=10.9206(2), c=17.4967(3), β=111.931(1)o, V=5438.65(14)3, Z=4, C46H52N6O25S2Tb2, Mr=1470.90, Dc=1.796 g/cm3, μ=2.747 mm-1, F(000)=2928, the final R= 0.0654 and wR=0.1322 for 3806 observed reflections with I > 2σ(I). In the neutral [Tb(SIP)(H2O)5]2 motif, the Tb(III) ions are linked by the SIP ligands to form a one-dimensional zigzag chain propagating along the c axis. The zigzag chains are linked together by hydrogen bonds and π-π stacking interactions to form a two-dimensional supramolecular framework. The uncoordinated bpy molecules act as pillars to extend the two-dimensional sheets into a distinctive pillared three-dimensional supramolecular structure through O-H···N hydrogen bonds. The photoluminescence of the complex was investigated at room temperature in the solid state.     

分子印迹化学发光传感器在线检测牛肉与鸡肉组织中残留的磺胺嘧啶

以分子印迹作为识别体,制成高灵敏度和高选择性的化学发光传感器在线检测牛肉与鸡肉组织中残留的磺胺嘧啶。磺胺嘧啶作为靶分子,通过悬浮聚合制备了1～10μm的分子印迹聚合物。将分子印迹聚合物装入聚四氟乙烯管中,作为固相萃取柱,并联在八通阀上,用于在线选择吸附磺胺嘧啶。在最佳条件下,测得磺胺嘧啶线性范围7.0×10–9～9.0×10–7g/mL,方法的检出限为(3σ)2×10–10g/mL,11次平行测定3.0×10–8g/mL的磺胺嘧啶溶液的化学发光强度相对标准偏差为3.4%。方法能够用于检测肉类产品中残留的磺胺嘧啶。     

A Dinuclear Dysprosium-2-quinolinecarboxylate-1,10-Phenanthroline Compound:Crystal Structure and Magnetism

A dinuclear dysprosium(III) compound,[Dy_2(μ_2-OH)_2(QLC)_4(1,10-phen)_2]·4H_2O(1)(QLC-= 2-quinolinecarboxylate and 1,10-phen = 1,10-phenanthroline),was synthesized and structurally and magnetically characterized.Compound 1 crystallizes in triclinic system,space group P1 with a = 10.9439(3),b = 11.2823(3),c = 12.2323(4) ?,α = 107.446(3),β = 91.700(3),γ = 91.511(2)°,V = 1439.25(8) ?~3,Z = 1,C_(64)H_(50)N_8O_(14)Dy_2,Mr = 1480.12,Dc = 1.708 g/cm3,μ = 2.653 mm-1 and F(000) = 734.The final R = 0.0366 and w R = 0.0736 for 5816 observed reflections with I 2σ(I).Compound 1 contains the mononuclear [Dy(QLC)_2(1,10-phen)] subunit formed from one 1,10-phen and two QLC-ligands chelating Dy(III) ion.Two mononuclear [Dy(QLC)_2(1,10-phen)] subunits are bridged by a pair of μ_2-OH groups to give a centrosymmetric dinuclear [Dy_2(μ2-OH)_2(QLC)4(1,10-phen)_2] with each Dy(III) ion being eight-coordinated.Detailed susceptibility measurements revealed that compound 1 does not show slow magnetic relaxation under zero direct-current field but exhibits field-induced slow magnetic relaxation under 2 kOe applied field.     

雷诺数效应对翼型抖振特性的影响

飞行器抖振是一种非线性气动弹性问题,当飞行器进入抖振阶段时,将会对飞行器的性能产生严重影响。而在跨声速条件下,激波附面层相互作用会诱导机翼抖振。本文开展了跨声速条件下翼型抖振特性雷诺数效应的实验研究,揭示了翼型跨声速抖振起始迎角、激波运动前缘边界、频谱特性、抖振频率与雷诺数变化的基本规律。结论如下:雷诺数变化会导致抖振起始边界的改变,对抖振起始迎角下的功率谱密度峰值有明显影响;随着雷诺数的增大,激波运动的前缘后移。雷诺数变化对抖振频率有明显影响,随着马赫数增大,雷诺数效应增强。     

A Luminescent Tb(Ⅲ)-4,4’,4’’-nitrilotribenzoate Compound with a Three-dimensional Structure

A coordination polymer of [Tb(ntb)]n(1) based on 4,4’,4’’-nitrilotribenzoate ligand(ntb3–) was synthesized. Compound 1 crystallizes in monoclinic system, space group C2/c with a = 13.7318(4), b = 27.5628(9), c = 5.4046(2) ?, β = 111.142(3)°, V = 1907.88(12) ?3, Z = 4, C21H12NO6Tb, Mr = 533.24, Dc = 1.856 g/cm3, μ = 3.745 mm–1, F(000) = 1032, the final R = 0.0184 and wR = 0.0456 for 1883 observed reflections with Ⅰ > 2s(Ⅰ). In compound 1, the eight-coordinated Tb(III) atoms are bridged by carboxylate groups of ntb3– ligands to generate a one-dimensional Tb-carboxylate chain, which is further linked by the ntb3– ligands to form a three-dimensional structure. Compound 1 exhibits characteristic Tb(Ⅲ) luminescent emissions in the solid state.     

Two Cd(Ⅱ)-biphenyl-3,3’-disulfonyl-4,4’-dicarboxylate-2,2’-bipyridine Compounds: Structures and Luminescence

Two coordination polymers based on the mixed ligands of biphenyl-3,3?-disul-fonyl-4,4?-dicarboxylate(BPDSDC4–)and 2,2?-bipyridine(2,2?-bpy),{[Cd(BPDSDC)0.5(2,2?-bpy)(H2O)]·(H2O)}n(1)and{[Cd(BPDSDC)0.5(2,2?-bpy)2]·(H2O)}n(2)were synthesized.Both compounds crystallize in the monoclinic system,space group P21/n.For 1,a=7.5737(2),b=17.4284(5),c=13.5982(5)?,β=90.788(3)°,V=1794.76(10)?^3,Z=4,C17H15N2O7SCd,Mr=503.77,Dc=1.864 g/cm^3,μ=1.378 mm^?1,F(000)=1004,the final R=0.0299 and wR=0.0644 for 3137 observed reflections with I>2s(I).For 2,a=13.3097(2),b=10.66240(10),c=17.6583(3)?,β=91.779(2)°,V=2504.74(6)?^3,Z=4,C27H21N4O6SCd,Mr=641.94,Dc=1.702 g/cm^3,μ=1.008 mm^?1,F(000)=1292,the final R=0.0244 and wR=0.0583 for 4594 observed reflections with I>2s(I).The Cd(II)atoms in both compounds are six-coordinated.In 1,the Cd(2,2?-bpy)units are connected by BPDSDC4–ligands to generate a one-dimensional(1D)ribbon structure.The 1D ribbons are linked by the hydrogen bonds and π···π interactions to give a three-dimensional(3D)structure.In compound 2,the Cd(2,2?-bpy)2 units are linked by the BPDSDC^4–ligands to form a 1D chain.Compounds 1 and 2 show luminescent emissions.     

In Situ Hydrothermal Synthesis of a Mononuclear Copper（Ⅱ） Complex： Cu（H2SIP-O）（bpy）（H2O） （H4SIP-O = 4-Hydroxyl-5-sulfoisophthalic Acid）

The mononuclear complex, Cu（H2SIP-O）（bpy）（H2O） （H4SIP-O = 4-hydroxyl- 5-sulfoisophthalic acid and bpy = 2,2＇-dipyridyl）, has been synthesized by the hydrothermal reaction of Cu（OH）2 with NaH2SIP and bpy at 160 ℃, and characterized by single-crystal X-ray diffraction, elemental analysis and IR spectrum. The new ligand 4-hydroxyl-5-sulfoisophthalic acid derived from 5-sulfoisophthalic acid ligand under an in situ hydrothermal condition. The crystal of the complex crystallizes in a triclinic system, space group P1, with a = 7.757（4）, b = 10.663（6）, c = 11.727（7）A, α = 94.272（4）, β = 104.067（7）, γ = 97.400（7）°, V= 927.4（9）A^3, Z = 2, C18H14N2O9SCu, Mr= 497.93, Dc= 1.783 g/cm^3,μ = 1.350 mm^-1, F（000） = 506, the final R = 0.0518 and wR = 0.1513 for 4180 observed reflections with I 〉 2σ（I）. The central Cu（II） ion is five-coordinated by two oxygen atoms from the H2SIP-O^2- ligand and two nitrogen atoms of bpy ligand in a distorted square-planar geometry as well as a water oxygen atom in the apical position to complete a distorted square-pyramidal coordination geometry. The mononuclear copper molecules are linked by hydrogen bonds between coordinated water molecules and sulfonate groups to form a one-dimensional double-chain structure. The chains are further held together through extensive π-π stacking interactions between the aromatic rings to form a three- dimensional supramolecular structure.     

浅谈速算式三算和儿童心理（节选）

珠心算的发现、发展乃至在国内外推广，经过了中国专家学者们几十年的发现、研究、实验、发展过程，也包括无数默默无闻的一线教师、教练们倾其心血、殚其精思、接踵接力的教学实践。这里刊登了尽瘁于珠心算教学讲坛上的山西平陆实验小学教学教师、著名珠心算专家陈子镜的得力助手王玉玲（传记载本期珠坛春秋栏目）的遗作节选，以飨读者……     

两个由1,1′-环己烷二乙酸构筑的镉的配合物的合成、晶体结构和荧光性质(英文)

通过邻羧苯乙酸、1,10-邻菲啰啉及硝酸镉的溶剂热反应合成了2个配合物:[Cd(phen)(chdc)]n(1)和[Cd(phen)(chdc)(H2O)]n(2)。X-射线单晶衍射显示:1是梯状双链结构;2是单链结构,单链再通过氢键连接成双链。虽然1和2的组分相似,但它们在固态条件下的荧光发射却大不一样,可能在光化学方面有潜在的应用。