Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

基于相移偏折法的高反射表面面形测量技术

利用单相机所采集的图像实现了对光滑高反射表面面形的直接检测.首先利用相机获取参考平面在标准平面镜中的镜像,然后通过参考平面上的点与归一化成像平面上图像点之间的密集折返对应关系,求得待测镜面的深度距离,从而实现对高反射表面面形的测量.通过光线追迹将该测量过程转化为求解物空间中关于两对应光线束之间的相交问题.以相位为载体获取面形梯度分布,求得该表面的法向量场,并求解相应的反射光线束.通过光线追迹对该光线束与相应入射光线束求“交点”检测高反射表面.对标准平面镜进行实验检测,测量得到的面形平面度为0.19 mm.采用传统方法与本文所提方法对汽车后视镜进行检测,所得检测结果对应点之间的平均距离为0.15 mm,验证了本文方法检测镜面面形的有效性.     

Study of blood collection and sample preparation for analysis of vitamin D and its metabolites by liquid chromatography–tandem mass spectrometry

The analysis of vitamin D status, with special emphasis on 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D, is gaining interest in clinical studies due to the classical and non-classical effects attributed to this prohormone. In this research, the influence of the two steps preceding determination (viz. sample collection and preparation) on the quantitative analysis of vitamin D and its more important metabolites has been studied. Two preparation approaches, deproteination and solid-phase extraction (SPE), have been evaluated in terms of sensitivity to delimit their application, thus establishing that detection of 1,25-dihydroxyvitamin D cannot be addressed by protein precipitation. Concerning sample collection, serum and plasma reported high accuracy (above 83.3%) for vitamin D and metabolites, while precision, expressed as relative standard deviation, was below 12.9% for all analytes in both samples. Statistical analysis revealed that serum and plasma provided similar physiological levels for vitamin D₃, 24,25-dihydroxyvitamin D₃ and 25-hydroxyvitamin D₃, while significantly different levels were obtained for 1,25-dihydroxyvitamin D₃, always higher in plasma than in serum. Sample collection and treatment have proved to be significant in the analysis of vitamin D and its relevant metabolites.     

Approximation of Functions by the Szász-Mirakjan-Kantorovich Operator

We characterize the approximation of functions in the L_p-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Iodine/persulfate-promoted site-selective direct thiolation of quinolones and uracils

A simple and general method for direct thiolation of 4-quinolones with disulfides or thiols under I₂/K₂S₂O₈ system has been developed. Under the optimal conditions, the C–S bond coupling can take place effectively with good to decent yields and excellent regioselectivity of the S-linked products. The established metal-free site-selective approach was also applicable to transform a range of uracil substrates to the thio-substituted products under mild conditions. Further transformation to the sulfone derivatives can be conveniently performed in one-pot. These easy-to-handle protocols represent a useful and interesting synthetic alternative with good substrate scope and functional group compatibility.     

Kaplansky’s “infinite abelian groups” and its two test problems

Abstract

Kaplansky’s Infinite Abelian Groups, originally published in 1954, has recently been republished. In recognition of its continuing significance after 65?years, the authors illustrate some important ideas and techniques described in the book. In particular, a class of groups is defined for which there are affirmative answers to the author’s two famous “Test Problems.”     

Direct synthesis of Poly(Ԑ-Caprolactone)-block-poly (glycidyl methacrylate) copolymer and its usage as a potential nano micelles carrier for hydrophobic drugs

Ring-opening (ROP) and enzymatic copolymerization (ECP) are among the most widely used approaches for synthesizing copolymers of polycaprolactone (PCL). It involves multiple-step reactions and the utilization of enzymes that make the process a lot more complicated, time consuming, and expensive. Atom transfer radical polymerization (ATRP) has been adopted to synthesize a novel amphiphilic copolymer in our study. The study presents a method to eliminate the ROP/ECP multiple steps in monomer polymerization thus making the process simpler and smoother. The synthesis of cationic polymer micelles copolymer of PCL-PGMA (polycaprolactone grafted poly glycidyl methacrylate) was carried out using direct functionalization of hydroxy group in crude PCL to achieve a higher degree of functionalization, i.e., 12.8% for macroinitiator. FTIR and ¹H-NMR confirmed the successful synthesis of the copolymer with better control over the molecular weight with a PDI (1.84). DSC and XRD results showed the reduction of crystallinity by 86.81%, making copolymer more compatible for drug delivery application. The synthesized copolymer was further converted to nano-micelles drug carrier having an average size of 96.08 ± 21.22 nm. The drug encapsulation efficiency achieved was 60.0 ± 1.7%, and nano-micelles rendered a slow and controlled release of naproxen with long-term storage stability.     

DMA-80测汞仪的应用探讨

本文的主要实验目的是利用DMA-80测汞仪直接测定固体样品中的汞并证明其方法可靠。采用升温加热直接进行热分解、金汞齐反应,采用长、短双检测池,可直接测定固体、液体样品,汞含量在0.n×10-9～600.0×10-9范围内的样品都能被很准确地测定,每个样品测定时间约为5min。 测试结果证明其方法具可靠性。     

Effect of Direct yellow 50 removal from an aqueous solution using nano bentonite; adsorption isotherm,kinetic analysis and also thermodynamic behavior

The developing countries are suffering from the toxicity of different industrial effluents, especially dyes that contaminate water systems. This study successfully explained the preparation and characterization of nano bentonite to extract Direct Yellow Fifty (DY50). Direct Yellow 50 is an organic contaminant that may affect the quality of water. The characterization of prepared nanoparticles was done using Scanning electron microscopy (SEM), X-ray diffraction (XRD), and Fourier-transform infrared (FTIR). The impact of different operating conditions was studied using different pH, dose, temperature, contact time, and initial DY50 concentrations. The obtained results indicated that nano bentonite could adsorb about 94 % at initial concentrations of 40 mg/L, respectively. The optimum removal conditions were observed at an acidic pH (pH 3) using a sorbent material dosage of 0.05 g for 4 h at 30 °C. The adsorption isotherm, kinetic analysis, and thermodynamic behavior were studied using linear equation form, and the adjusted R² was compared to detect the preferred models. The adsorption behavior pseudo-second order kinetics, and fitted Langmuir isotherm model, respectively, showed the chemisorption interactions between adsorbed and sorbed molecules. Thermodynamic behavior indicated that the reaction was exothermic. Finally, this study strongly recommended using nano bentonite for DY50 removal from an aqueous solution.