Thermoanalytical characterization of polyphenylacetylene: III. Use of modulated differential scanning calorimetry (MDSC)

Four polyphenylacetylene samples, synthesized using different C₆H₅OH/Mo molar ratios, were investigated thermoanalytically by modulated temperature differential scanning calorimetry (MTDSC) in order to clarify a non-reversible exothermic event observed between 473 and 523 K on normal DSC. A stepwise, non-reversible change in heat capacity suggests the presence of internal reactions within the sample, that are followed by decomposition with loss of volatile products.     

Study of a Catalytic Mechanism in Additive Differential Pulse Techniques

The new electrochemical double pulse technique, known as additive differential normal pulse voltammetry (ADNPV) when there is no restriction on the duration of both pulses, and additive differential pulse voltammetry (ADPV) when t₂?t₁, has been applied to a pseudo‐first‐order catalytic mechanism. The expressions obtained here are applicable to planar and spherical electrodes, of any radius. This is of great interest since the size of the electrode plays an important role in the preponderating of diffusive and kinetics processes. The signal obtained with this technique presents the same morphological characteristics as the triple pulse technique, double differential pulse voltammetry (DDPV) and is more advantageous than DDPV and than the double pulse one, differential pulse voltammetry (DPV).     

Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

Necessary and sufficient conditions are established in this paper for the existence of positive- and/or negative-definite solutions to the algebraic Riccati equation with indefinite coefficient. An iterative procedure is also given for computing such a solution.Project supported by the National Science Foundation of China and by the special program of the State Education Commission of China under grant 9033507.     

Differential Expression Analysis of Single-Cell RNA-Seq Data: Current Statistical Approaches and Outstanding Challenges

With the advent of single-cell RNA-sequencing (scRNA-seq), it is possible to measure the expression dynamics of genes at the single-cell level. Through scRNA-seq, a huge amount of expression data for several thousand(s) of genes over million(s) of cells are generated in a single experiment. Differential expression analysis is the primary downstream analysis of such data to identify gene markers for cell type detection and also provide inputs to other secondary analyses. Many statistical approaches for differential expression analysis have been reported in the literature. Therefore, we critically discuss the underlying statistical principles of the approaches and distinctly divide them into six major classes, i.e., generalized linear, generalized additive, Hurdle, mixture models, two-class parametric, and non-parametric approaches. We also succinctly discuss the limitations that are specific to each class of approaches, and how they are addressed by other subsequent classes of approach. A number of challenges are identified in this study that must be addressed to develop the next class of innovative approaches. Furthermore, we also emphasize the methodological challenges involved in differential expression analysis of scRNA-seq data that researchers must address to draw maximum benefit from this recent single-cell technology. This study will serve as a guide to genome researchers and experimental biologists to objectively select options for their analysis.     

The Kinetics of Formation of Microporous Polytriazine in Diphenyl Sulfone

This study highlights the value of nonisothermal kinetic methods in selecting temperature conditions for the isothermal preparation of microporous polymeric materials. A dicyanate ester is synthesized and the kinetics of its polymerization in diphenyl sulfone are studied by calorimetry under nonisothermal conditions. The kinetics are analyzed by a model-based approach, using the Kamal model, as well as by a model-free approach, using an advanced isoconversional method. Both approaches correctly predict the time to completion of polymerization at a given temperature. The material prepared independently at the predicted temperature is characterized by electron microscopy and CO₂ adsorption measurements and is confirmed to possess a microporous structure with a multimodal distribution of micropores with two major maxima at ~0.5 and 0.8 nm.     

Radiation damage by soft β-particles self-irradiation of β-tritiated polystyrene

The effect of self-irradiation of β-tritiated polystyrene under high vacuum at 25°C was studied, and simultaneous random chain scission and cross-linking were observed. Analyses of the gaseous products and the colored polymer residue showed that hydrogen was the only volatile product, while spectroscopic measurements indicated that the coloration was associated with the presence of main-chain double bonds.

G values for hydrogen formation GH₂, cross-linking, G _XL and chain scission, G _CS were obtained as follows: GH₂=0.031; G _CS=0.044; G _XL=0.061. Possible mechanisms of radiation damage are discussed.     

镓一镁二元相图研究

本文用两种差热分析方法即“一步法”和“二步法”以及多晶X-射线衍射法对镓-镁二元系相图进行了研究.修正了前人的工作. 为了考察该二元体系的金属间化合物是否以镓原子多面体簇状结构存在,作者对富镓部分相图(镓原子百分含量大于71.4％)进行了较为细致的研究.在三种不同比例下(含镓量分别为85at.％、90at.％、95at.％)合成,分离得到了颗粒状晶体.对这些晶体进行了差热分析和多晶X-射线研究.分析结果表明:从这三种不同比例的合金中分离得到的晶体为同一金属间化合物Mg_2Ga_5,也是该二元系镓含量最高的金属间化合物.考察Ga-Mg体系中存在的五种金属间化合物的结构,未能发现镓原子以多面体簇状结构存在的现象.     

非线性灰色微分方程(dx)/(dt)+ax~(■a)=b 的拟合

本文给出了拟合非线性灰色微分方程 dx/dt+ax~(■a)=b 的计算方法,并讨论了它的性质及应用.     

具转向点常微分方程混合边值问题的一致收敛差分格式

本文得到了具转向点的二阶常微分方程混合边值问题解的导数估计,提出了Il′in型差分格式,证明了此差分格式按L~1模关于小参数ε的一阶一致收敛性。最后,给出了一个数值例子,计算结果与理论分析一致。     

Equations of attainable set dynamics,part 1: Integral funnel equations

In control theory, there is growing interest in the evolution of sets, especially attainable sets at timet. This is caused due to their applications to control under uncertainty, optimal control, and differential games. Recently, a new mathematical theory for attainable set evolution was developed. It is based on the concept of approximate localization, instead of differentiation. Here, we give a generalization of this theory.