关于周期函数的最小正周期的存在性

我知道一些周期函数在定义域上存在最小正周期 ,如ｓｉｎｘ ,ｃｏｓｘ ,ｔａｎｘ ,ｃｏｔｘ等 .但有些周期函数如常值函数、狄利克莱函数等均没有最小正周期 .那么 ,什么样的周期函数一定存在最小正周期呢 ?笔者至今未见有结果 .本文利用极限和函数连续的性质 ,给出了周期函数存在最小正周期的充分条件 .引理 1　设 {ａｎ}为数列 ,且ａｎ >0 ,ｌｉｍｎ∞ａｎ =0 .则对任意实数Ａ ,存在由 {ａｎ}的前ｎ项构成的整系数线性组合数列 {Ａｎ},其中Ａｎ=α1 ａ1 α2 ａ2 … αｎａｎ(ａｉ为整数 ,ｉ=1 ,2… ,ｎ) ,使得ｌｉｍｎ∞ Ａｎ=Ａ .…     

国产SY-01型液相色谱仪气动泵的改进

SY-01型液相色谱仪目前虽已停止生产,但有不少单位购有此种仪器,并仍在使用。该仪器的气动泵易出故障,主要是因为使用的电子元件质量欠佳,使气动泵电气部件失灵。另外气动泵中使用两个交流电磁阀,因交变电流使铁芯振动,易使上阀门橡皮部份损坏而漏气或粘住。我们针对上述两方面的弊病对气动泵进行改进。改进中省去了气动泵电气部件,克服了这部份易出故障的弊病;将气动泵的两个交流电磁阀的     

齿轮啮合的数学理论及应用简介

<正> 自1972年以来,我们在和有关工程技术人员的接触中,他们提出了不少与微分几何有关的运动学的问题,其中以齿轮的传动和切削等问题较为突出.由此引起了我们对这方面问题的注意.我们总结了有关问题及有关资料,认为首先应该研究啮合原理的数学基础,在1972—1974年期间写出了《齿轮啮合理论的数学基础》一文;后来又在这个理     

Dark blue erenkov second harmonic generation in the two-layer-stacked hexagonal periodically poled MgO:LiNbO_3s

We report the dark blue nonlinearˇCerenkov radiation by the second harmonic generation(SHG)in a two-layer-stacked hexagonal periodically-poled-MgO:LiNbO3s(PPMgOLNs).Based on the direct wafer bonding of two target PPMgOLNs rotating around the axis perpendicular to the plane with an angle of 30°,twelve bright spots as twice of those in a single PPMgOLN are shown at each second-harmonicˇCerenkov ring.The experimental results agree with the theoretical ones and present a promising application in the fabrication of three-dimensional(3D)PPMgOLNs.     

Nonequilibrium thermodynamics and fluctuation relations for small systems

In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti–Cohen fluctuation theorem, and then to the Evans–Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.     

爆炸冲击震动模拟平台的研制

为了模拟核爆、化爆冲击震动环境,根据能量守恒和弹性碰撞原理,研制了悬挂式爆炸冲击震动模拟平台。该平台能够完成水平向和垂直向冲击试验,通过对锤重、锤高和垫层厚度等参数的合理选择,性能指标可达到:水平向冲击加速度峰值5~1 500 m/s2,作用时间50~4 ms;垂直向冲击加速度峰值10~1 000 m/s2,作用时间60~4 ms。性能试验表明,该平台能够为防护工程结构抗震及其他有关冲击振动问题的研究提供安全、方便、经济、可靠的试验手段。     

Prototype studies on the forward MWDC tracking array of the external target experiment at HIRFL-CSR

A prototype of the forward tracking array consisting of three multiwire drift chambers (MWDC) for the external target experiment (CEE) at the Heavy Ion Research Facility at the Lanzhou -Cooling Storage Ring (HIRFL-CSR) has been assembled and tested using cosmic rays. The signals from the anode wires are amplified and fed to a Flash-ADC to deliver the drift time and charge integration. The performances of the array prototype are investigated under various high voltages. For the tracking performances, after the space-time relation (STR) calibration and the detector displacement correction, the standard deviation of 223 μm of the residue is obtained. The performances of the forward MWDCs tracking array meets the requirements of CEE in design.     

S型叶尖小翼对风轮近尾迹声辐射影响的实验研究

采用5因素5水平的正交实验方法,找到在不同尖速比下均具有较好功率放大效果的S型叶尖小翼结构,对其影响近尾迹流动与声辐射的特征进行了测试。发现该小翼可以打散从风轮叶尖脱落的叶尖涡结构,在测试方位面内形成多个涡量集中区域,而且使叶尖涡内高涡量区域减小,降低叶尖涡的强度。同时,该小翼还可以使叶尖附近的压力脉动衰减,高压力脉动区域缩小,降低声辐射的强度,有效降低近尾迹中的声压级,靠近风轮附近测点的最大声压级降幅超过10dB,在1倍风轮直径下游位置的声压级降幅为2~7 dB.对S型叶尖小翼影响近尾迹流动和声辐射的研究,为提高风力机性能和降噪途径的探索积累了经验.