最大公约数的和与最小公倍数的和

设正整数j不大于n,我们给出计算最大公约数的和g(n)=■(j,n)与最小公倍数的和L(n)= ■[j,n]的计算公式.     

集合环和的性质

给出了元素属于集合环和的充分必要条件、集合交与集合环和的关系、由仅属于n个集合之一的元素所构成的集合与集合环和的关系,得出了仅属于3个集合之一的元素所构成集合的基数公式.     

Evolution of magnetic and superconducting fluctuations with doping of high-Tc superconductors

Electronic Raman scattering from high- and low-energy excitations was studied as a function of temperature, extent of hole doping, and energy of the incident photons in Bi2Sr2CaCu2O8+/-delta superconductors. For underdoped superconductors, short-range antiferromagnetic (AF) correlations were found to persist with hole doping, and doped single holes were found to be incoherent in the AF environment. Above the superconducting (SC) transition temperature Tc, the system exhibited a sharp Raman resonance of B1g symmetry and energy of 75 millielectron-volts and a pseudogap for electron-hole excitations below 75 millielectron-volts, a manifestation of a partially coherent state forming from doped incoherent quasi particles. The occupancy of the coherent state increases with cooling until phase ordering at Tc produces a global SC state.     

Dependence of upper critical field and pairing strength on doping in cuprates

We have determined the upper critical field Hc2 as a function of hole concentration in bismuth-based cuprates by measuring the voltage induced by vortex flow in a driving temperature gradient (the Nernst effect), in magnetic fields up to 45 tesla. We found that Hc2 decreased steeply as doping increased, in both single and bilayer cuprates. This relationship implies that the Cooper pairing potential displays a trend opposite to that of the superfluid density versus doping. The coherence length of the pairs xi(0) closely tracks the gap measured by photoemission. We discuss implications for understanding the doping dependence of the critical temperature Tc0.     

极限函数与和函数的关系及其连续性

给出极限函数与和函数的定义．讨论了极限函数与和函数之间的关系,利用极限函数得到函数项级数收敛的一个必要条件,研究了极限函数与和函数的连续性,得到部分和函数列连续的一个充分条件．     

Disentangling the electronic and phononic glue in a high-Tc superconductor

Unveiling the nature of the bosonic excitations that mediate the formation of Cooper pairs is a key issue for understanding unconventional superconductivity. A fundamental step toward this goal would be to identify the relative weight of the electronic and phononic contributions to the overall frequency (?)-dependent bosonic function, Π(?). We performed optical spectroscopy on Bi(2)Sr(2)Ca(0.92)Y(0.08)Cu(2)O(8+δ) crystals with simultaneous time and frequency resolution; this technique allowed us to disentangle the electronic and phononic contributions by their different temporal evolution. The spectral distribution of the electronic excitations and the strength of their interaction with fermionic quasiparticles fully account for the high critical temperature of the superconducting phase transition.     

具有极值拟亏量和的无穷级亚纯函数

讨论了具有极值拟亏量和的亚纯函数的亏量和问题,把有穷级超越亚纯函数推广到无万级亚纯函数,得到了两个无穷级亚纯函数关于极值拟亏量和的结果.定理1 设f为开平面上无穷级亚纯函数,如果存在正整数l使∑a∈C(⊕)l)(a,f)=2(l+1)/l-(⊕)l)(∞,f),则∑a∈(C-)δ(a,f)=0,即f没有亏值.定理2 设f为开平面上无穷级亚纯函数,如果存在正整数l使∑a∈C(⊕)l)(a,f)=l+1/l(2-(⊕)(∞,f)),则∑a∈Cδ(a,f)=0,即f没有有穷的亏值.     

两个三角函数积的和的封闭形和式

利用发生函数的方法,研究了三角函数序列:∑nk=0dkcos(kα+φ)与∑nk=0(-1)kdksin(kα+φ),得到了其封闭形和式计算公式和正负相间封闭形计算公式,其次利用复数隶莫佛公式给出两个三角函数积的和式∑nk=0cos(kα+φ)sinkβ,∑nk=0(-1)ksin(kα+φ)coskβ封闭形计算公式.     

高校品牌竞争优势及其法则

为增强学校的竞争实力,通过对高教市场特征的分析,阐明新形势下高校品牌竞争优势,并从校长领导、办学特色、品牌营销等方面选择相对竞争优势等策略,提出要以异分性为切入点树品牌形象、借鉴企业化经营管理模式改善学校教育管理的品牌市场竞争法则。     

小麦赤霉病预测模型及规则的探讨

运用模糊数学理论,用3个具有较好指示性的气象预报因子,建立了贴近度合成运算模型,并结合富阳市小麦赤霉病的实际发生情况,设定贴近度预测规则。实践表明,该技术不仅回测拟合率高,而且取得了连续2年的试报成功。     

关于部分和之和乘积的注记

设{X,Xn,n≥1}是独立同分布的正的均方可积的随机变量序列,μ=E(X)>0,σ2=Var(X),变异系数γ=σ/μ,记Tn=∑nk=1kXk,得到了∏Nn=1Tn在某种正则化因子下的极限分布.     

关于部分和之和乘积的注记

设{X,Xn,n≥1)是独立同分布的正的均方可积的随机变量序列,μ=E(X)>0,σ2=Var(X),变异系数γ=σ/μ,记Tn=(∑nk=1)kXk,得到了(∏Nn=1)Tn在某种正则化因子下的极限分布.     

Nearly singular magnetic fluctuations in the normal state of a high-Tc cuprate superconductor

Polarized and unpolarized neutron scattering was used to measure the wave vector- and frequency-dependent magnetic fluctuations in the normal state (from the superconducting transition temperature, Tc = 35 kelvin, up to 350 kelvin) of single crystals of La1.86Sr0.14CuO4. The peaks that dominate the fluctuations have amplitudes that decrease as T-2 and widths that increase in proportion to the thermal energy, kBT (where kB is Boltzmann's constant), and energy transfer added in quadrature. The nearly singular fluctuations are consistent with a nearby quantum critical point.     

Thermal diffusivity and conductivity of lunar material

The thermal diffusivity and conductivity of type C lunar samples returned by Apollo 11 are lower and less dependent on temperature than those of type A samples. The thermal properties of both types are lower than the corresponding properties of normal terrestrial rocks.     

残差和为零的非线性回归法及其应用

指出传统拟线性回归和近代非线性最小二乘回归存在的问题,以及有截距的线性回归和无截距的线性回归之间的差别;提出通过附加残差和为零的强制条件改进非线性最小二乘回归的思想和方法,即残差和为零的非线性回归,并从理论上和实验数据上证明其优越性.得出的结论和结果为:对于幂函数、指数函数、双曲函数、对数函数和S型曲线等非线性函数,通...     

Regional-scale assembly rules and biodiversity of coral reefs

Tropical reef fishes and corals exhibit highly predictable patterns of taxonomic composition across the Indian and Pacific Oceans. Despite steep longitudinal and latitudinal gradients in total species richness, the composition of these key taxa is constrained within a remarkably narrow range of values. Regional-scale variation in reef biodiversity is best explained by large-scale patterns in the availability of shallow-water habitat. Once habitat area is accounted for, there is surprisingly little residual effect of latitude or longitude. Low-diversity regions are most vulnerable to human impacts such as global warming, underscoring the urgent need for integrated management at multinational scales.     

任意角铺设复合材料层合板位移及层间应力有限元的计算

利用基于整体-局部位移假设的1,2-3高阶理论的位移有限单元,对任意角铺设复合材料层合板位移及层间应力进行数值计算,计算结果表明,基于此高阶理论的位移有限单元不仅能很好地计算层合板位移,也能较好地计算横向剪切应力。     

任意角铺设复合材料层合板位移及层间应力有限元的计算

利用基于整体-局部位移假设的1,2-3高阶理论的位移有限单元,对任意角铺设复合材料层合板位移及层间应力进行数值计算,计算结果表明,基于此高阶理论的位移有限单元不仅能很好地计算层合板位移,也能较好地计算横向剪切应力。