Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage

We establish large sample approximations for an arbitrary number of bilinear forms of the sample variance–covariance matrix of a high-dimensional vector time series using ${?}_1$-bounded and small ${?}_2$-bounded weighting vectors. Estimation of the asymptotic covariance structure is also discussed. The results hold true without any constraint on the dimension, the number of forms and the sample size or their ratios. Concrete and potential applications are widespread and cover high-dimensional data science problems such as tests for large numbers of covariances, sparse portfolio optimization and projections onto sparse principal components or more general spanning sets as frequently considered, e.g. in classification and dictionary learning. As two specific applications of our results, we study in greater detail the asymptotics of the trace functional and shrinkage estimation of covariance matrices. In shrinkage estimation, it turns out that the asymptotics differ for weighting vectors bounded away from orthogonality and nearly orthogonal ones in the sense that their inner product converges to 0.     

The acute toxicity of tri-n-butyltin glycocholate

The oral acute toxicity for tri-n-butyltin glycocholate (TBT-GA), a newly synthesized organotin steroid, was determined using Long Evans rats. The compound was suspended in corn oil and adminstered by gavage using standard techniques. Unlike tri-n-butyltin taurocholate, which exhibited two different toxicities, one for the tri-n-butyltin moiety and one for the taurocholic acid moiety, the TBT-GA exhibited a single toxicity, that of the whole molecule. The LD₅₀ value was 213 mg kg^?1 (0.274 mmol kg), which on a millimolar basis is similar to that observed for other tri-n-butyltin compounds. The dead rats exhibited distended stomachs, enlarged ceca, and lesions in the intestinal tract. The actual cause of death could not be positively identified. Animals that survived more than three days also exhibited time- and dose-related atrophy of the thymus gland. With 36% more male than female rats succumbing to TBT-GA, the chemical appears to be more toxic towards male than female rats.     

Latent tracks generated in micro-crystalline α-L-alanine and standard bone powder by Co ion beams as investigated by EPR-method

Latent tracks created by ⁵⁹Co ions in l-α-alanine and standard bone powder were examinated by EPR-method. For 3.4 MeV/amu cobalt ions the mean radius of tracks (considered as the distance from the ion path on which a detectable concentration of paramagnetic centers exists) was estimated as (190±30) Å for l-α-alanine and (220±30) Å for bone powder.     

非线性Sobolev Galpern方程的近似惯性流形

近似惯性流形概念与耗散偏微分方程的长时间行为研究有关, 该文对非线性Sobolev Galpern方程构造了两个近似惯性流形. 证明了非平滑近似惯性流形Σ和平滑近似惯性流形Σ_0=P_mH对整体吸引子有相同的逼近阶数.     

Liquid-liquid biphasic synthesis of long chain wax esters using the Lewis acidic ionic liquid choline chloride·2ZnCl2

The first liquid-liquid biphasic synthesis of wax esters in a Lewis acidic ionic liquid, choline chloride·2ZnCl₂ by the esterification of long chain carboxylic acids with long chain alcohols is described. The reported reaction system has the advantages of both homogeneous and heterogeneous catalysis with high product yield and the ease of product as well as catalyst separation without the use of an organic solvent. The ionic liquid studied plays the dual role of solvent as well as catalyst and is recycled up to six times without any significant loss of activity.     

HL-1装置长脉冲放电的初步分析

本文初步分析了HL-1装置物理调试中获得的长脉冲放电的性质,简化模型计算结果与现有实验数据符合较好。初步判断,长脉冲放电尾部主要是逃逸电流。并提出了下一步工作的若干建议。     

Distinction between normal and leukemic bone marrow by water protons nuclear magnetic resonance relaxation times

Pulsed nuclear magnetic resonance studies have been carried out on bone marrow of normal human subjects and patients with leukemia: chronic myeloid leukemia (CML) and acute myeloid leukemia (AML). It was observed that the proton spin-lattice relaxation time (T₁) value was discriminatory in the normal and leukemic cases with a statistical significance of (p < 0.01). Ouabain treatment of cells did not show any perceptible change of T₁ value when compared with the nontreated cells, indicating that the concomitant cation effluxes do not affect spin-lattice relaxation time. The water contents of normal, leukemic, and ouabain treated cells were in the range 60%–80%. Higher Fe levels were encountered in the normal than the leukemic samples, while levels of Zn, Cu, Mn, Co, and Ni were elevated in the leukemic samples compared with the normals. Despite the T₁ differences observed, the multiparameter studies do not uniquely pinpoint factors responsible for the elevation of T₁ in the malignant state.     

Treatment of long‐term stored DNA—Comparison between different methods to obtain high‐quality material

Long‐term stored DNA can be sometimes the only source of genetic material of an organism that does not exist anymore, but a research interest still persists. However, there is a lack of information about useful methods to improve quality from such type of material. In this study, we compared four different protocols using DNA samples collected in 1998. Fresh DNA was also tested aiming to check the differences between these two material types. Sixteen samples of each DNA type treated with phenol‐chloroform with PEG 5.0%, silica‐gel membrane spin column, PEG 7.5%, and glass‐fiber matrix spin column were submitted to spectrophotometer measurements, electrophoresis, PCR, and RFLP‐PCR to assess the best method concerning yield, quality, and purity. Based on the results, purification with PEG 7.5% was considered the best method to treat aged DNA samples. In addition to the efficiency, this protocol has low cost. Analyzing the data, we also conclude that long‐term stored DNA may be considered a reliable and potential resource for future molecular studies.     

HE－1型催化剂异相聚合乙烯结晶性能研究 Ⅱ．超高分子量PE结晶行为

用小角Ｘ－射线散射，广角Ｘ－射线衍射，差示扫描量热法，研究了ＨＥ－１型钛系催化剂异相聚合超高分子量聚乙烯的稀溶液的结晶和熔融结晶的熔点，熔化热，结晶度，长周期，晶区厚度和非昌区厚度随分子量与结晶温度的关系．并着重讨论了熔融结晶和初生态结晶的不同过程机理．结果表明：ＵＨＭＷＰＥ稀溶液结晶的结晶度（Ｘｃ％），长周期（Ｌ）和晶区厚度（Ｌｃ）与分子量Ｍｗ无关，随结晶温度升高而增加，非晶区厚度（Ｌａ）与分子量和结晶温度均无关，熔点Ｔｍ随分子量增大稍有升高．熔融结晶样品长周期与分子量无关，却和结晶温度和时间有关．其结晶度和晶区厚度随分子量增大而下降，非昌区厚度和熔点均随分子量增大而增大，初生态粉末中没发现长周期，却发现有较高熔点．     

环磷酰胺诱导的小鼠骨髓细胞微核率的时间、剂量-效应观察

为研究环磷酰胺(CP)诱导的小鼠骨髓细胞微核率的时间-效应关系和剂量-反应关系,给小鼠一次腹腔注射不同剂量(按体质量计)CP(0、30、60、90 mg/kg)后,于不同时间(给药后12、24、36、486、0 h)、不同部位(胸骨与股骨)取材来观察小鼠骨髓细胞微核率的变化。结果表明,高、中、低三个剂量组的小鼠骨髓细胞微核率与0 mg/kg组相比较,其差异具有统计学意义(P<0.01),且4个剂量组之间两两比较也均有统计学意义(P<0.05),并表现出明显的剂量-反应关系;不同取样时间对小鼠骨髓细胞微核率的影响具有统计学意义(P<0.05),在36~48 h这个时间段能够观察到更高的微核率,通过线性回归的曲线拟合分析,以41 h取材最佳;胸骨取材与股骨取材之间的微核率差异无统计学意义(P>0.05)。环磷酰胺可作为诱导小鼠骨髓细胞微核的阳性对照,在一定范围内,具有剂量-反应关系和时间-效应关系。给小鼠一次腹腔注射量(按体质量计)60~90 mg/kg后36~48 h胸骨取材可取得较高微核率,结果满意。