A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Pyrolysis Analysis and Kinetics of Crude Oils

This research presents the results of an experimental study on the determination of pyrolysis behaviour and kinetics of six crude oils by differential scanning calorimetry (DSC) and thermogravimetry (TG/DTG). Crude oil pyrolysis indicated two main temperature ranges where loss of mass was observed. The first region between ambient to 400°C was distillation. The second region between 400 and 600°C was visbreaking and thermal cracking. Arrhenius-type kinetic model is used to determine the kinetic parameters of crude oils studied. It was observed that as crude oils gets heavier (°API decreases) cracking activation energy increases. Activation energy of cracking also show a general trend with asphaltene content. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Randomly transitional phenomena in the system governed by Duffing's equation

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.     

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.     

Duffing振子微弱信号检测方法的统计特性研究

利用混沌振子可以检测极其微弱的信号，并且具有很多优点，本文根据随机微分方程理论，通过对噪声经过Ｄｕｆｉｉｎｇ系统后统计特性的分析，确定了采用此方法检测的信噪改善比，从而为该方法的实际应用提供了指导，并且，本文针对周期系数线性微分方程的特点，提出了其输出统计特性的求法。     

BER Performance of Frequency Domain Differential Demodulation OFDM in Flat Fading Channel

A closed form expression for the bit error rate (BER) performance of frequency domaindifferential demodulation(FDDD) for orthogonal frequency division multiplexing system in flat fadingchannel is derived.The performance is evaluated by computer simulation and compared with the timedomain differential demodulation(TDDD).The results indicate that the performance of FDDD is betterthan that of TDDD,and the lower band of BER in the former is lower than that of the latter.     

频谱分析中的微分法与微分方程法

本文讨论了应用于傅里叶变换的微分性质的隐含假设,并叙述了信号不满足隐含假设时的修正方法。本文还给出了作为信号生成系统的微分方程描述,它使信号谱成为其生成系统的频率传递函数,指出了微分方程法的隐含假设。最后还给出了信号违反此假设时进行修正的方法。