CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENTIABLE FUNCTION DEFINED BY QUINARY DECIMAL

In this paper, we construct some continuous but non-differentiable functions defined by quinary decimal, that are Kiesswetter-like functions. We discuss their properties, then investigate the Hausdorff dimensions of graphs of these functions and give a detailed proof.     

正交变换在重积分中某些应用

正交变换是代数学的基本内容 ,其用途十分广泛 .重积分的计算往往存在技术性的困难 ,若利用“正交变换”的有关理论去解决某些重积分的计算问题是颇有功效的 .本文将以“正交变换”为工具 ,简洁的处理重积分的某些问题     

Hardy's inequality and the boundary size

We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.

     

The elastic theory of a single DNA molecule

We study the elastic responses of double-(ds) and single-stranded (ss) DNA at external force fields. A double-strand-polymer elastic model is constructed and solved by path integral methods and Monte Carlo simulations to understand the entropic elasticity, cooperative extensibility, and supercoiling property of dsDNA. The good agreement with experiments indicates that short-ranged base-pair stacking interaction is crucial for the stability and the high deformability of dsDNA. Hairpin-coil transition in ssDNA is studied with generating function method. A threshold force is needed to pull the ssDNA hairpin patterns, stabilized by base pairing and base-pair stacking, into random coils. This phase transition is predicted to be of first order for stacking potential higher than some critical level, in accordance with experimental observations.     

正确的答案错误的解法

有些题目即使解法不正确,也可能得出正确的答案. 如果注意了答案对但解法错的情况,让学生判别其正误,那么对于物理概念的理解、物理规律的掌握、思维能力的提高都将起重要作用. 例l 重10N的均匀木棒AB长为L,B端放在地面上,A端用竖直的绳子吊起(图     

Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence

 We study the half-space problem of the nonlinear Boltzmann equation, assigning the Dirichlet data for outgoing particles at the boundary and a Maxwellian as the far field. We will show that the solvability of the problem changes with the Mach number ℳ^∞ of the far Maxwellian. If ℳ^∞<−1, there exists a unique smooth solution connecting the Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the far Maxwellian. Otherwise, such a solution exists only for the Dirichlet data satisfying certain admissible conditions. The set of admissible Dirichlet data forms a smooth manifold of codimension 1 for the case −1<ℳ^∞<0, 4 for 0<ℳ^∞<1 and 5 for ℳ^∞>1, respectively. We also show that the same is true for the linearized problem at the far Maxwellian, and the manifold is, then, a hyperplane. The proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight. Received: 20 April 2002 / Accepted: 4 December 2002 Published online: 21 March 2003 Communicated by H.-T. Yau     

Formation of p-type ZnO film on InP substrate by phosphor doping

ZnO thin film was initially deposited on InP substrate by radio frequency (rf) magnetron sputtering and the diffusion process was performed using the closed ampoule technique where Zn₃P₂ was used as the dopant source. To verify the junction formation of ZnO thin films, the electrical properties were measured, and the effects of Zn₃P₂ diffusion on ZnO thin films were investigated. It is observed that the electrical property of the film is changed from n-type to p-type by dopant diffusion effect. Based on the results, it is confirmed that ZnO thin films can be a potential candidate for ultraviolet (UV) optical devices.     

Bush连续不可微函数的分形性质

本文对用递推关系确定的Bush连续不可微函数,找出了迭代函数系(IFS),从而得到它的级数表达式和所具有的自仿射分形的有关性质.最后还计算出函数图象的Hausdorff 维数的准确值.     

从一道运动学题目的求解谈坐标系选取的重要性

通过比较一道典型运动学题目的近似求解方法与精确求解方法，探讨坐标系选取对研究曲线运动的重要性．     

Gauged harmonic maps,Born‐Infeld electromagnetism,and magnetic vortices

We study maps from a 2‐surface into the standard 2‐sphere coupled with Born‐Infeld geometric electromagnetism through an Abelian gauge field. Such a formalism extends the classical harmonic map model, known as the σ‐model, governing the spin vector orientation in a ferromagnet allows us to obtain the coexistence of vortices and antivortices characterized by opposite, self‐excited, magnetic flux lines. We show that the Born‐Infeld free parameter may be used to achieve arbitrarily high local concentration of magnetic flux lines that the total minimum energy is an additive function of these quantized flux lines realized as the numbers of vortices antivortices. In the case where the underlying surface, or the domain, is compact, we obtain a necessary sufficient condition for the existence of a unique solution representing a prescribed distribution of vortices antivortices. In the case where the domain is the full plane, we prove the existence of a unique solution representing an arbitrary distribution of vortices and antivortices. Furthermore, we also consider the Einstein gravitation induced by these vortices, known as cosmic strings, establish the existence of a solution representing a prescribed distribution of cosmic strings cosmic antistrings under a necessary sufficient condition that makes the underlying surface a complete surface with respect to the induced gravitational metric. © 2003 Wiley Periodicals, Inc.