Abstract:
While atomic force microscopy (AFM) has been increasingly applied to life science, artifactual measurements or images can occur during nanoscale analyses of cell components and biomolecules. Tip-sample convolution effect is the most common mechanism responsible for causing artifacts. Some deconvolution-based methods or algorithms have been developed to reconstruct the specimen surface or the tip geometry. Double-tip or double-probe effect can also induce artifactual images by a different mechanism from that of convolution effect. However, an objective method for identifying the double-tip/probe-induced artifactual images is still absent. To fill this important gap, we made use of our expertise of AFM to analyze artifactual double-tip images of cell structures and biomolecules, such as linear DNA, during AFM scanning and imaging. Mathematical models were then generated to elucidate the artifactual double-tip effects and images develop during AFM imaging of cell structures and biomolecules. Based on these models, computational formulas were created to measure and identify potential double-tip AFM images. Such formulas proved to be useful for identification of double-tip images of cell structures and DNA molecules. The present studies provide a useful methodology to evaluate double-tip effects and images. Our results can serve as a foundation to design computer-based automatic detection of double-tip AFM images during nanoscale measuring and imaging of biomolecules and even non-biological materials or structures, and then personal experience is not needed any longer to evaluate artifactual images induced by the double-tip/probe effect.

Abstract:
The features of the large Cluster projects’ management processes, complexity, “one-off” and “irreversibility”, make the projects’ process knowledge hard to be expressed, analyzed and obtained accurately. It is also not convenient to be accumulated and disseminated, and can’t be learned and used by managers. However, such knowledge is the crystallization of human wisdom. It has an important role in promoting efficiency of projects management and increasing accumulation of social knowledge. A better way is needed to find for its representation and utilization. From the perspective of cluster project management department, this article takes a cluster project’s construction as an example, and proposes a suitable method for the process knowledge representation in large cluster projects’ management processes, combined with the Topic Maps and MFFC-Ⅱ & MLD-Ⅱ.

Abstract:
This paper mainly explored the strategies of capacity-building for the poor in the early stage of tourism development in poverty-stricken areas. Given the requirements of tourism poverty alleviation, the capacity-building strategies during the transition period need to focus on non-school-age and impoverished population, and integrate both explicit and tacit knowledge, as well as absorb foreign advanced knowledge adequately, while some limitations still exist in the literatures now. In this paper, we analyzed the cross-group knowledge transfer process of “migrant workers-local poor people” to explore the capacity-building strategies that meet various requirements during the transitional period for the poor.

Abstract:
We introduce simple prescriptions of the Yukawa potential to describe the effect of size polydispersity and macroion shielding effect in charged colloidal systems. The solid-liquid phase boundaries were presented with the Lindemann criterion based on molecular dynamics simulations. Compared with the Robbins-Kremer-Grest simulation results, a deviation of melting line is observed at small $\lambda$, which means large macroion screening length. This deviation of phase boundary is qualitatively consistent with the simulation result of the nonlinear Poisson-Boltzmann equation with full many-body interactions. It is found that this deviation of the solid-liquid phase behaviour is sensitive to the screening parameter.

Abstract:
For the continuous-time and the discrete-time three-state hidden Markov model, the flux of the likelihood function up to 3-dimension of the observed process is shown explicitly. As an application, the sufficient and necessary condition of the reversibility of the observed process is shown.

Abstract:
If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a normal but nonsymmetric Ornstein-Uhlenbeck operator $L$ on the complex Wiener space. The eigenfunctions of the operator $L$ are given. In addition, the hypercontractivity for the nonsymmetric Ornstein-Uhlenbeck semigroup is shown.

Abstract:
We present the product formula for complex multiple Wiener-Ito integrals. As applications, we show the Ustunel-Zakai independent criterion, the Nourdin-Rosinski asymptotic moment-independent criterion and joint convergence criterion for complex multiple Wiener-Ito integrals.

Abstract:
Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators in the complex Hilbert space $L_{\Cnum}^2(\mu)$. We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown.

Abstract:
In this paper, a product formula of Hermite polynomials is given and then the relation between the real Wiener-It\^{o} chaos and the complex Wiener-It\^{o} chaos (or: multiple integrals) is shown. By this relation and the known multivariate extension of the fourth moment theorem for the real multiple integrals, the fourth moment theorem (or say: the Nualart-Peccati criterion) for the complex Wiener-It\^{o} multiple integrals is obtained.

Abstract:
For an indecomposable $3\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means of an alternate parameterization of the transition rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids calculating matrix logarithm or matrix square root. In addition, an implicit description of the imbedding problem for the $3\times 3$ stochastic matrix in Johansen [J. Lond. Math. Soc., 8, 345-351. (1974)] is pointed out.