Abstract:
The method of Laplace transforms is used to findthe distribution function, mean, and variance ofthe number of renewals of a renewal processwhose inter-arrival time distribution has a rational Laplace transform.Where the Laplace transform is not rational,we use the Padéapproximation method.We apply our method to certain examples andthe results are compared to those reported byother researchers.

Abstract:
Heat conduction in 1-dimensional anharmonic systems is anomalous in the sense that the conductivity \kappa scales with a positive power of the system size, \kappa ~ L^\alpha. In two dimensions, previous simulations and theoretical arguments gave a logarithmic divergence. For rectangular systems of size L_\| x L_\perp there should be a cross-over from the 2-d to the 1-d behaviour as the aspect ratio r = L_\| / L_\perp increases from r=1 to r >> 1. When taking periodic boundary conditions in the transverse direction, this should be of direct relevance for the heat conduction in single-walled carbon nanotubes. In particular, one expects that k nanotubes of diameter R should conduct heat better than a single nanotube of the same length and of radius kR. We study this cross-over numerically by simulating the Fermi-Pasta-Ulam model. Apart from giving a precise estimate of the exponent \alpha, our most intriguing results are that the divergence does not seem to be logarithmic in d=2 but also power-like, and that the cross-over does not happen at a fixed aspect ratio. Instead, it happens at r=r^* with r^* -> \infty for L -> \infty.

Abstract:
In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension. We show that the following is true: Let $F(x) = (x,f(x)), x \in \mathbb{R}^{n}$ be a graph solution to the soliton equation $$ \bar{H}(x) + F^{\bot}(x) = 0. $$ Assume $\sup_{\mathbb{R}^{n}}|Df(x)| \le C_{0} < + \infty$. Then there exists a unique smooth function $f_{\infty}: \mathbb{R}^{n}\to \mathbb{R}^k$ such that $$ f_{\infty}(x) = \lim_{\lambda \to \infty}f_{\lambda}(x) $$ and $$ f_{\infty}(r x)=r f_{\infty}(x) $$ for any real number $r\not= 0$, where $$ f_{\lambda}(x) = \lambda^{-1}f(\lambda x). $$

Abstract:
Han recently discovered new hook length identities for binary trees. In this paper, we extend Han's identities to binomial families of trees. Moreover, we present a bijective proof of one of the identities for the family of ordered trees.

Abstract:
In this work, we propose a fast and energy-efficient neighbor discovery scheme for proximity-aware networks such as wireless ad hoc networks. Discovery efficiency is accomplished by the use of a special discovery signal that provides random multiple access with low transmit power consumption and low synchronization requirement.

Abstract:
The credit of agriculture-related organizations has a stronger dynamic uncertainty than the general main credit. Although the traditional assessment model can evaluate the main credit from different aspect, it stresses the independence of the object and forced the uncertainty into the certainty to deal with. These methods do not suit for the agriculture-related organizations which have loosely organized and extensive internal links. This paper presents the set of the set of theoretical to integrate the existing assessment model. Also the paper established the credit risk assessment model suit for agriculture-related organization. The research should have some theoretical value and practical significance for the assessment of credit risk of agriculture-related organizations. Key words: Set of theoretical; Agriculture-related organization; Credit risk; Assessment model

Abstract:
This paper aims to reveal the mechanism of Collateralized Debt Obligations (CDOs) and how CDOs extend the current global financial crisis. We first introduce the concept of CDOs and give a brief account of the de-velopment of CDOs. We then explicate the mechanism of CDOs within a concrete example with mortgage deals and we outline the evolution of the current financial crisis. Based on our overview of pricing CDOs in various existing random models, we propose an idea of modeling the random phenomenon with the feature of heavy tail dependence for possible implements towards a new random modeling for CDOs.

Abstract:
A laboratory-scale plasma spout-fluid bed reactor with a 10 kW DC plasma torch was developed and tested using quartz sand particle and rice hull. The preliminary experimental results including particle recirculation and attrition, bed temperature distribution and stability, as well as biomass gasification system energy balance were presented in this paper. Research results indicated that plasma spout-fluid bed reactor may be a technically feasible reactor for carbonaceous organic material gasification.

Two techniques for
exploring relative horizontal accuracy of complex linear spatial features are
described and sample source code (pseudo code) is presented for this purpose.
The first technique, relative sinuosity, is presented as a measure of the
complexity or detail of a polyline network in comparison to a reference
network. We term the second technique longitudinal root mean squared error
(LRMSE) and present it as a means for quantitatively assessing the horizontal variance
between two polyline data sets representing digitized (reference) and derived
stream and river networks. Both relative sinuosity and LRMSE are shown to be
suitable measures of horizontal stream network accuracy for assessing quality
and variation in linear features. Both techniques have been used in two recent
investigations involving extraction of hydrographic features from LiDAR
elevation data. One confirmed that, with the greatly increased resolution of
LiDAR data, smaller cell sizes yielded better stream network delineations,
based on sinuosity and LRMSE, when using LiDAR-derived DEMs. The other
demonstrated a new method of delineating stream channels directly from LiDAR
point clouds, without the intermediate step of deriving a DEM, showing that the
direct delineation from LiDAR point clouds yielded an excellent and much better
match, as indicated by the LRMSE.