A reproducing kernel method for solving nonlocal fractional boundary value problems

In our previous works, we proposed a reproducing kernel method for solving singular and nonsingular boundary value problems of integer order based on the reproducing kernel theory. In this letter, we shall expand the application of reproducing kernel theory to fractional differential equations and present an algorithm for solving nonlocal fractional boundary value problems. The results from numerical examples show that the present method is simple and effective.     

Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations

In this paper, we establish a new composition theorem about Stepanov-like pseudo almost automorphic functions under the local Lipschitz condition. Using this composition theorem, we also study the existence and uniqueness of pseudo almost automorphic solutions for nonautonomous evolution equations. Our results extend many recent known ones on these topics.     

Effects of Unequal Couplings on Fidelity of a Quantum Controlled-Controlled-Not Gate

By numerically solving the Sch6dinger equation of a three-nuclear-spin system, the effects of the non-uniform nearest-neighbor （NN） interaction on the fidelity of a quantum controlled-controlled-no （CCN） gate are investigated for a digital initial state and a superposition initial state respectively. It is found from our simulation that the ratio of the deviation of the NN coupling δJ to the NN coupling J should be smaller than 0.0005 to ensure a high fidelity of the quantum CCN gate.     

Brane effects on extra-dimensional scenarios: a tale of two gravitons

We analyze the propagation of a scalar field in multidimensional theories which include kinetic corrections in the brane, as a prototype for gravitational interactions in a four-dimensional brane located in a (nearly) flat extra-dimensional bulk. We regularize the theory by introducing an infrared cutoff given by the size of the extra dimensions, R, and a physical ultraviolet cutoff of the order of the fundamental Planck scale in the higher-dimensional theory, M. We show that, having implemented cutoffs, the radius of the extra dimensions cannot be arbitrarily large for M≳1 TeV. Moreover, for finite radii, the gravitational effects localized on the brane can substantially alter the phenomenology of collider and/or table-top gravitational experiments. This phenomenology is dictated by the presence of a massless graviton, with standard couplings to the matter fields, and a massive graviton which couples to matter in a much stronger way. While graviton KK modes lighter than the massive graviton couple to matter in a standard way, the couplings to matter of the heavier KK modes are strongly suppressed.     

MWCNTs复合物纳米流体的摩擦学性能

将油性剂油酸(OA)填充进多壁碳纳米管(MWCNTs)的空腔内制备复合物,再以复合物为添加剂制备一种纳米流体,考察了复合物的质量分数、MWCNTs的酸处理时间以及摩擦测试条件等对纳米流体摩擦学性能的影响,并分析了复合物的润滑机理. 结果表明:油酸被成功填充到经酸处理的MWCNTs管内,填充率约20%;摩擦过程中,复合物制备的纳米流体的摩擦系数有不断减小趋势,其减摩效果甚至优于同等含量的油酸乳化液;当复合物的质量分数为0.1%左右时,纳米流体可获得最佳的减摩、抗磨效果;随着酸化处理时间的增加,复合物制备的纳米流体的减摩、抗磨性能会有所提高. 摩擦过程中,复合物可释放出油酸并形成润滑膜,MWCNTs则能够在油酸形成的润滑膜上发挥“微轴承”的作用,从而使复合物获得更加优良的减摩、抗磨效果.      

Calorimetric evidence of antiferromagnetism in GdBa2Cu3O6+δ

Heat capacity measurements between 1.8 and 10K have been made on the superconductor GdBa₂Cu₃O_6+δ with δ ⋍ 0.7 and T_c ⋍ 94K. A well defined magnetic transition prevails at 2.22K. The entropy involved agrees well with the complete antiferromagnetic ordering of Gd³⁺ ions.     

方波信号的傅里叶分解实验

选择通用设备，建立了一个简易的周期信号傅里叶分析系统，通过其测试了方波信号各谐波成份的频率和幅度值，验证了方波信号的傅氏展开关系．     

Uniqueness of entire functions

Let f be a nonconstant entire function and let a be a meromorphic function satisfying T(r,a)=S(r,f) and a?a′. If f(z)=a(z)⇔f′(z)=a(z) and f(z)=a(z)⇒f″(z)=a(z), then f≡f′, and a?a′ is necessary. This extended a result due to Jank, Mues and Volkmann.     

Temperature dependence of transport behavior of a short DNA molecule

DNA molecules may work as novel devices due to their interesting electronic transport properties. We here propose a theoretical method to deal with the temperature dependence of the transport behavior of a short DNA molecule, taking into account Coulomb interaction of electrons and the coupling between electrons and the two-level system in the DNA molecule. The nonlinear current-voltage curves are derived by using the Landauer formulae. We find that the voltage gap of the current-voltage curves is sensitive to the parameters of the two-level system. We also find that Coulomb blockade peaks can be controlled by varying the temperature, which relates to particular features of the DNA molecule.     

复局部β-凸空间l~β与L~β[0,1]的共轭锥的次表示定理

本文研究复局部β-凸空间l~β与L~β[0,1](0<β<1)的共轭锥(l~β)_β~*与(L~β[0,1])_β~*的构造与表示问题,得到(l~β)_β~*(?)mM_β~+(T),(L~β[0,1])_β~*(?)L~∞M_β~+(I×T),称为(l~β)_β~*与(L~β[0,1])_β~*的次表示定理。