含三角函数的函数值域

孟建业(1945—),男,北京市人,河北省特级教师含有三角函数的复合函数值域,在各类试题中经常出现,这类题常涉及代数中函数与方程、几何中元素间的相关位置等内容.下面就若干常见题型加以归纳.1　直线型形如ｆ(ｘ)=ａｓｉｎｘ ｂ的函数,我们可以将它看作是定义在[-1,1]上的?..     

Bursting and spiking due to additional direct and stochastic currents in neuron models

Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter $V_{\rm K}$ in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ``circle/homoclinic" bursting and the integer multiple ``fold/homoclinic" bursting with one spike per burst, as well as the transition from integer multiple bursting to period-1 ``circle/homoclinic" bursting and that from stochastic ``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are investigated in detail.     

氨基乙硫醇修饰金电极直接测定芦丁含量的研究

利用分子自组装技术制备氨基乙硫醇修饰金电极,并采用脉冲伏安法直接测定芦丁的含量。以pH7.0的乙醇和磷酸盐混合缓冲溶液作底液,芦丁在氨基乙硫醇修饰金电极上于0.19 V(vs.SCE)处呈现一灵敏的氧化电流峰,峰电流和芦丁的浓度在8.0~2.5×102μmol/L范围内呈良好的线性关系。由于抗坏血酸在氨基乙硫醇修饰金电极上的氧化电位出现显著负移,因此,可避免抗坏血酸对芦丁检测的干扰。本方法可以不经预分离直接检测药物中芦丁含量。     

A systematical study of the chiral magnetic effects at the RHIC and LHC energies

Considering the magnetic field response of the QGP medium,we perform a systematical study of the chiral magnetic effect(CME),and make a comparison with the experimental results for the background-subtracted correlator H at the energies of the RHIC Beam Energy Scan(BES)and the LHC energy.The CME signals from our computations show a centrality trend and beam energy dependence that are qualitatively consistent with the experimental measurements of the charge dependent correlations.The time evolution of the chiral electromagnetic current at the RHIC and LHC energies is systematically studied.The dependence of the time-integrated current signal on the beam energy√s with different centralities is investigated.Our phenomenological analysis shows that the time-integrated electromagnetic current is maximal near the collision energy√s≈39 GeV.The qualitative trend of the induced electromagnetic current is in agreement with the CME experimental results at the RHIC and LHC energies.     

电化学氧化增强金属钴卟啉的自组装研究

应用电化学方法将钴(Ⅱ)卟啉氧化成钴(Ⅲ)卟啉以增强它与4-巯基吡啶(MP)自组装膜的轴向配位作用,从而快速制备了有序钴卟啉自组装修饰电极CoTMPP/MP/Au(E).电化学石英晶体微天平(EQCM)测试证实电化学氧化对钴卟啉膜生长过程的增强作用.Ram an光谱及修饰电极电催化还原氧研究显示,该修饰电极与经过长时间浸渍法得到的CoTMPP/MP/Au(I)修饰电极具有完全相似的有序结构和性质.与直接将钴卟啉吸附在电极表面的CoTMPP/Au修饰电极相比,以巯基吡啶为桥键得到的钴卟啉修饰电极具有更好的电催化活性和稳定性.     

基于脱乙酰基魔芋葡甘聚糖固定酶的葡萄糖传感器

制备了脱乙酰基魔芋葡甘聚糖(d-KGM)的溶胶-凝胶,用红外光谱表征了其脱乙酰基前后的结构转化.探讨了d-KGM溶胶-凝胶的制备条件对其成膜性能及酶固定化的影响.在此基础上将d-KGM用于电极表面葡萄糖氧化酶的固定,制备了相应的葡萄糖传感器,并对传感器的工作条件进行了优化.所制备的传感器灵敏度为240 nA/mmol/L,线性范围为0.1～8 mmol/L,表观米氏常数KM为19.6 mmol/L,稳定性好,寿命长.实验结果表明d-KGM是一种可用于生物传感器中酶固定化的优良材料.     

取向PET薄膜偶极热松弛的研究

用纵拉、先纵后横、纵-横-纵等拉伸方式得到了各种平面取向程度的PET薄膜。短路热释电流温谱显示α峰随平面取向度增大向高温线性移动。被冻结的大分子主链链段偶极热松弛活化能随反式构象含量增大呈线性下降。热松弛时间常数则随反式构象含量增大而增长。     

二溴甲烷的同步辐射光电离研究

采用５０～２００ｎｍ同步辐射光，对ＣＨ２Ｂｒ２的光电离过程进行了研究，根据测定的母体离子及其碎片离子出现势，得到二溴甲烷的绝热电离势为１０．２３±０．０１ｅＶ，并获得了离子的生成焓，解离能及键能等热力学数据，分析了碎片离子的光解离电离通道。     

水热法制备纳米ZnS的光催化性能研究

采用水热法制备了结晶良好的ZnS纳米粒子,通过XRD、FT-IR、TEM、UV-Vis DRS等手段对所合成的ZnS粉体的结构、粒度和理化性能进行表征,并以亚甲基蓝为目标降解物,评价了ZnS粉体在紫外光和可见光下的光催化性能。研究结果表明,水热法制备的纳米ZnS为典型的六方晶系,粒径大致为10～20 nm,不论是在紫外光或可见光下对亚甲基蓝均具有优异的脱色率,呈现出良好的光催化性能。     

电沉积硅烷分子印迹膜修饰电极的制备及其应用

以3,4-二羟基苯甲酸作模板分子,在玻碳电极表面恒电位沉积四甲氧基硅烷和苯基三甲氧基硅烷,经无水乙醇将模板分子洗脱,制得硅溶胶-凝胶分子印迹膜电极.该电极能有效地抑制电化学氧化过程中3,4-二羟基苯甲酸的电聚合及其同分异构体2,4-二羟基苯甲酸对测定的干扰.实验表明,该修饰电极对3,4-二羟基苯甲酸测定的线性浓度范围为1.0×10-5~8.0×10-4mol.L-1,浓度检测下限为5.0×10-6mol.L-1.