数学物理方程中的通解问题

通过例证说明,通解法对于偏微分方程而言,其适用范围要比通常认为的大.并表明,只要适当变通,行波法就可用于有界情况.     

Preparation and characterization of ZnO nanorods from NaOH solutions with assisted electrical field

ZnO naorods on ZnO-coated seed substrates were fabricated by solution chemical method from Zn(NO₃)₂/NaOH under assisted electrical field. The working mechanism of electrical field was analyzed and the factors affecting the rod growth such as potential, precursor concentration and growth temperature were elucidated. The structural and optical properties are characterized by SEM, TEM, XRD, HRTEM and UV-vis. The results indicated that the nanorods have wurtzite structure without electrical field and are primarily of zincite structure under electrical field; when the electrical field is 1.1-1.3 V, not only the elevation of ion diffusion and adsorption lower the crystallite/solution interfacial energy and then the crystal nucleation barrier by increasing charge intensity, but also the production of H⁺ through oxidation of OH⁻ increases properly the degree of solution supersaturation near the substrate, and thus lowers the activation energy. Both the two processes do favor to rod growth. With increasing precursor concentration in this system, the average diameter and length of ZnO nanorods increase, leading to decreasing of optical transmittance. The maximum rod growth rate at given concentration of Zn²⁺ occurs at a specific temperature.     

OnQ-order andR-order of convergence

We give sufficient conditions for a sequence to have theQ-order and/or theR-order of convergence greater than one. If an additional condition is satisfied, then the sequence has an exactQ-order of convergence. We show that our results are sharp and we compare them with older results.This work was supported in part by the National Science Foundation under Grant No. DMS-85-03365. The author wishes to thank J. E. Dennis and R. A. Tapia for helpful comments, and the referee for pointing out a number of typographical and mathematical errors in the original version of this paper.     

Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach

Based on the Dyson-Schwinger equations of QCD in the "rainbow" approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phonon density of states of ann-component alloy

We have generalized the coherent potential approximation (CPA) of Tripathi and Behera to the case of ann-component alloy. It is seen that then-component CPA density of states reproduces the binary, ternary quartenary alloys etc when the appropriate limits are adopted.     

对2005年高考试题中关于螺旋测微计实验试题的解析与拓展

解析了2005年普通高等学校全国联考(理综卷)中考察螺旋测微计原理的实验填空题,并给出了3方面的拓展:不常见的游标卡尺、圆弧游标、具有游标的螺旋测微计.     

用干涉方法测量薄膜应力

基于基片弯曲法和牛顿环的基本原理,使用He-Ne激光器、扩束镜、凸透镜和带分光镜的移测显微镜,搭建了薄膜应力测量装置.采用直流溅射法制备了厚度为30~144 nm的银薄膜,衬底采用厚度为0.15 mm、直径为18 mm的圆形玻璃片.实验发现,薄膜厚度对银薄膜的内应力有显著的影响,在薄膜厚度很小时,随着薄膜厚度的增加,应力迅速增大,达到最大值后,随着厚度的继续增加,薄膜应力下降较快并趋于稳定值.