The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

用环形扩散管和滤纸联用采样技术采集空气中氨和铵盐

建立了环形扩散管和滤纸采样夹联用，分形态同时采集空气中所态氨和颗粒态铵盐的方法。在同一气流中，采用涂渍１．５％草酸乙醇水溶液的环形扩散管采集气态氨，用浸渍上述试剂的玻璃纤维纸和慢速定量滤纸分别采集颗粒安和第一层滤纸上的铵盐挥发产生的氨气。用靛酚蓝比色法分别测定氨和铵盐。当采气流速为１．０Ｌ／ｍｉｎ时，采样效率高于９８．２％。将本法测得的氨气和铵盐的总量与标准采样方法的测定结果比较。无显著性差异（Ｐ     

Preparation and Characterization of Nanotitanium Dioxide Coating Film Doped with Fe^3＋ Ions on Porous Ceramic

The nanotitanium dioxide （TiO2） photocatalytic and porous ceramic filtering technique is one of the advanced methods to effectively treat organic wastewater. The TiO2 sol doped with Fe^3＋ ions was prepared by sol-gel processing. The influences of the process conditions of coating nanophotocatalytic material- Fe^3＋-TiO2 film on the surface of porous ceramic filter by dipping-lift method on the performance of porous ceramic filter were studied. The porous ceramic filters have two functions at the same time, filtration and photocatalytic degradation. The results of this study showed that the pH and viscosity of the sol, amount of Fe^3＋ ions doped as well as the coating times greatly affect the quality of coating film, the performance parameters and the photocatalytic activity of the porous ceramic filter. When the pH of the sol is 3-4, the viscosity is about 6 mPa.S, the amount of doped Fe^3＋ ions is about 2.0 g/L, the porous ceramic filter has been shown to have the best filtering performance and photocatalytic activity. In this condition, the porosity of porous ceramic is about 42.5%, the pore diameter is 8-10μm. The degradation of methyl-orange is 74.76% under lighting for 120 rain.     

改进的单纯形优化法用于混合稀土的同时测定

本文应用改进的单纯形优化法较好地弥补了目前在分析化学计量学中得到广泛应用的卡尔曼滤波法所存在的不足，交法应用于混合稀土的同时测定中，获得了满意的结果，结果准确度较卡尔滤波法的有显著的提高。     

Determination of trace elements in ambient aerosol samples

A microwave-assisted digestion procedure using HNO₃, HF, and H₂O₂ has been developed for analysis of elements in ambient particulate matter (PM). The samples are collected on cellulose filters and analyzed by inductively coupled plasma mass spectrometry (ICP-MS). The ICP-MS is calibrated with external standards, and recovery of analytes is tested with NIST SRM 1648 Urban Dust. This method has been used to quantify the airborne concentrations of a large number of elements, including Ag, As, Ba, Be, Ca, Cd, Ce, Co, Cr, Cs, Cu, Fe, Ga, K, Li, Mg, Mn, Mo, Ni, Pb, Rb, Se, Sb, Sr, Ti, Tl, V, and Zn. For the majority of these elements, recovery of the NIST SRM is within 15% of the certified values.     

Synthesis and Electrochemical Studies of Spinel LiNi1−xMnxVO4

Spinel compound LiNi_1−xMn_xVO₄ (0≤x≤0.4) had been prepared by using the moist chemical method. X-ray diffraction spectra showed that the lattice constant increased with x in the LiNi_1−xMn_xVO₄, XPS spectra indicating that Li1s had a chemical shift towards lesser binding energy, and manganese in LiNi_1−xMn_xVO₄ existing as the mixed valence of Mn²⁺ and Mn³⁺. The electrochemical charge and discharge testing at a current density of 0.1 mA/cm² between the potentials of 4.0 and 3.0 V vs Li/Li⁺ in 1 mol/dm³ LiPF₆/EC+DEC (1:1 by volume) at 25°C showed that LiNi_1−xMn_xVO₄ cell has a better rechargeability, but a lower cell voltage of 4.0 V vs Li/Li⁺ than that without the doping sample, and the capacity and the cycle efficiency of the Li/LiNi_1−xMn_xVO₄ cells increased with x in the LiNi_1−xMn_xVO₄.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

Pretreatment of swine wastewater using anaerobic filter

Efforts were made to assess the efficiency of an anaerobic filter packed with porous floating ceramic media and to identify the optimum operational condition of anaerobic filter as a pretreatment of swine wastewater for the subsequent biological removal of nitrogen and phosphorus. A stepwise decrease in hydraulic retention time (HRT) and an increase in organic loading rate (OLR) were utilized in an anaerobic filter reactor at mesophilic temperature (35°C). The optimum operating condition of the anaerobic filter was found to be at an HRT of 1 d. A soluble chemical oxygen demand (COD) removal efficiency of 62% and a total suspended solids removal efficiency of 39% at an HRT of 1 d were achieved with an OLR of 16.0 kg total COD/(m³·d), respectively. The maximum methane production rate approached 1.70 vol of biogas produced per volume of reactor per day at an HRT of 1 d. It was likely that the effluent COD/total Kjeldahl nitrogen ratio, of 22, the COD/total phosphorous ratio of 47, and the high effluent alkalinity >2500 mg/L as CaCO₃ of the anaerobic filter operated at an HRT of 1 d was adequate for the subsequent biological removal of nitrogen and phosphorus.     

反相悬浮聚合法合成超强吸水剂

以两性高分子作悬浮稳定剂，用反相悬浮聚合法合成了聚（丙烯酸盐－丙烯酰胺）类超强吸水剂．研究了交联剂、稳定剂、引发剂等用量、中和程度、单体组成及链转移剂等聚合条件对吸水剂吸水性能的影响．得到了吸蒸馏水１０５０ｍＬ／ｇ及吸０．９％ＮａＣｌ溶液８６ｍＬ／ｇ的超强吸水剂．此外，还比较了含不同反离子的聚丙烯酸类吸水剂的吸水性能