Searching for a counterfeit coin with b-balance

We consider the classical problem of searching for a heavier coin in a set of n coins, n-1 of which have the same weight. The weighing device is b-balance which is the generalization of two-arms balance. The minimum numbers of weighings are determined exactly for worst-case sequential algorithm, average-case sequential algorithm, worst-case predetermined algorithm, average-case predetermined algorithm.We also investigate the above search model with additional constraint: each weighing is only allowed to use the coins that are still in doubt. We present a worst-case optimal sequential algorithm and an average-case optimal sequential algorithm requiring the minimum numbers of weighings.     

Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing

We studied the influence of focusing depth on the index change threshold and damage threshold of silica glass irradiated by a focused 120 fs laser beam. Both thresholds increased with the focusing depth. The aspect ratio of the waveguide cross section can be selected by changing the focusing depth. A 5 mm long waveguide was written at the depth of 2100 μm, which was single mode at 632.8 nm and exhibited propagation loss of 0.56 dB/cm. The refractive index change was calculated to be ∼2.47×10^-3. The influence of the focusing depth should be considered in multi-layer devices as shown in the fabrication of a 3×3 waveguide array. PACS 42.62.-b; 42.82.Et; 81.05.Kf     

我国税收收入超GDP增长的原因分析

文章依据我国近年来税收增长和GDP增长的统计数据，得出税收增长速度高于GDP增长速度的客观事实，并就其原因进行了综合分析，最后指出，从长远来看我国未来的税收增长必将回归到与经济同步增长或者略低于经济增长的轨道上来，以为政府决策提供参考。     

Difference in micellar properties of sodium dodecyl sulfonate from sodium 4-decyl naphthalene sulfonate in D2O solution studied by 1H NMR relaxation and 2D NOESY

¹H chemical shift changes of sodium 4-decyl naphthalene sulfonate (SDNS) at 313 K show that its critical micellar concentration lies between 0.82 and 0.92 mmol/dm³, which is in the same range as that of the previous study at 298 K. The spin–lattice relaxation time, spin–spin relaxation time and two-dimensional nuclear Overhauser enhancement spectroscopy experiments give information about the structure of the SDNS micelle and the dynamics of the molecules in the micelle. The size of the SDNS micelle remains almost unchanged in the temperature range from 298 to 313 K as deduced by analyzing the self-diffusion coefficient. Special arrangement of the naphthyl rings of SDNS in the micelles affects the packing of these hydrophobic chains. The methylene groups of the alkyl chain nearest the naphthalene groups penetrate into the aromatic region, which results in a more tightly packed hydrophobic micellar core than that of sodium dodecyl sulfonate.     

激光水下偏振特性用于目标图像探测

利用激光水下偏振特性获得偏振差分图像(PDI),并运用PDI技术,从理论和实验上对水下目标探测进行了研究.介绍了PDI基本概念和实验系统原理,然后比较分析了不同条件下普通图像与PDI在辨别目标距离及其纹理上的差别和PDI中背景偏振光的影响,得出利用目标和背景偏振光的差异区分二者,从而提高探测距离的结论,并取得了较好的效果.在此基础上提出了通过处理有关PDI偏振参量来进一步辨别目标与背景的设想.     

L3C宇宙线实验中Z0数据的分析

μ子动量谱的精确测量是L3C宇宙线实验最重要的目标之一.事例重建的好坏是该测量的关键,而能量确定的衰变为双μ子的事例是检验重建程序的最好手段.该数据分析利用在2000年中获取的数据作为样本,筛选出了LEP在2000年4月、5月、8月和9月等Z⁰能量运行期间L3C宇宙线实验数据中记录的Z⁰→μ⁺μ^－事例数据,得到通过重建程序后动量为45GeV的μ子动量分辨率为(5.4?7±0.25)%.     

第Ⅰ种强度不对称三态叠加多模叠加态光场N次方Y压缩—第一正交相位分量的压缩情况

根据量子力学中的线性叠加原理,构造了由三个强度不等的多模相干态光场|{Z_j^(A)}>_q、|{Z_j^(B)}>_q和|{Z_j^(C)}>_q的线性叠加所组成的第Ⅰ种强度不对称三态叠加多模叠加态光场|ψ_l^(ABC)>_q.利用多模压缩态理论,研究了态|ψ_l^(ABC)>_q的第一正交方分量(即磁场分量)的广义非线性等幂次N次方Y压缩特性.结果发现:①在上述各多模相干态光场中各模的强度和各模的初始相位各不相等的情况下,态|ψ_l^(ABC)>_q的第一正交分量-磁场分量在一定的条件下,总可呈现出周期性变化的、任意等幂次的N次方Y压缩效应;②当上述各多模相干态光场的强度和各模的初始相位相等时,态|ψ_l^(ABC)>_q的磁场分量的N次方Y压缩现象消失,态|ψ_l^(ABC)>_q可恒处于等幂次N-Y最小测不准态.