Averaging approximation to singularly perturbed nonlinear stochastic wave equations

An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq n\leq 3$\,. Here $\nu>0$ is a small parameter characterising the singular perturbation, and $\nu^\alpha$\,, $0\leq \alpha\leq 1/2$\,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $\nu$, u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of \ord{\nu^\alpha}\,.Comment: 16 pages. Submitte

Efficient Processing Node Proximity via Random Walk with Restart

Graph is a useful tool to model complicated data structures. One important task in graph analysis is assessing node proximity based on graph topology. Recently, Random Walk with Restart (RWR) tends to pop up as a promising measure of node proximity, due to its proliferative applications in e.g. recommender systems, and image segmentation. However, the best-known algorithm for computing RWR resorts to a large LU matrix factorization on an entire graph, which is cost-inhibitive. In this paper, we propose hybrid techniques to efficiently compute RWR. First, a novel divide-and-conquer paradigm is designed, aiming to convert the large LU decomposition into small triangular matrix operations recursively on several partitioned subgraphs. Then, on every subgraph, a “sparse accelerator” is devised to further reduce the time of RWR without any sacrifice in accuracy. Our experimental results on real and synthetic datasets show that our approach outperforms the baseline algorithms by at least one constant factor without loss of exactness

The Optimization of Jaw Crusher with Complex Motion Aimed at Reducing Stroke Feature Value of Its Outlet

Volume 8 Issue 1 (January 201

Diversity of eukaryotic plankton of aquaculture ponds with Carassius auratus gibelio, using denaturing gradient gel electrophoresis

PCR-denaturing gradient gel electrophoresis (DGGE) and canonical correspondence analysis (CCA) were used to explore the relationship between eukaryotic plankton community succession and environmental factors in two aquaculture pond models with gibel carp Carassius auratus gibelio. The main culture species of pond 1 were gibel carp and grass carp, and the combined density was 46224 fingerling/ha (gibel carp/grass carp/silver carp/bighead carp, 17:4:6:1). The main culture species of pond 2 was gibel carp, and the combined density was 37551 fingerling/ha (gibel carp/silver carp/bighead carp, 52:1:1). Water samples were collected monthly. The results showed that the annual average concentrations of TP and PO_4-P in pond 1 were significantly higher than pond 2 (p>0.05). The concentration of chlorophyll a (chl a) has no significantly difference between pond 1 and pond 2. DGGE profiles of 18S rRNA gene fragments from the two ponds revealed that the diversity of eukaryotic plankton assemblages was highly variable. 91 bands and 71 bands were detected in pond 1 and pond 2, respectively. The average Shannon–Wiener index of pond 1 was significantly higher than pond 2. Canonical correspondence analysis (CCA) revealed that temperature played a key role in the structure of the eukaryotic plankton community in both ponds, but the nutrient concentration did not affect it. Our results suggest that DGGE method is a cost-effective way to gain insight into seasonal dynamics of eukaryotic plankton communities in culture ponds, and the increase in the number of filter-feeding silver carp and bighead carp could increase the diversity of the eukaryotic plankton community

Effect of Relief-hole Diameter on Die Elastic Deformation during Cold Precision Forging of Helical Gears

During cold precision forging of helical gears, the die experiences high forming pressure resulting in elastic deformation of the die, a main factor affecting dimensional accuracy of a formed gear. The divided flow method in material plastic deformation is an effective way to reduce the forming force and the die pressure during cold precision forging of helical gears. In this study, by utilizing the flow-relief-hole method, a billet design with different initial diameters of the relief-hole is developed to improve the dimensional accuracy of cold forging gears. Three-dimensional Finite Element (FE) models are established to simulate the plastic deformation process of billet during cold precision forging of a helical gear and to determine the forming force acting on the die. Further models of die stress analysis are developed to examine the die elastic deformation and distribution of the displacement. Effects of the relief-hole diameters on die elastic deformation are studied. The results show that the elastic deformation of the die is different in the addendum, dedendum, and involute parts of forging gear using different relief-hole diameters. The die elastic deformation increases firstly and then decreases when the relief-hole diameter increases. The tooth portions are of larger elastic deformation and the peak value locates in the addendum. It shows the importance of optimizing the relief-hole diameter to minimize the dimensional inaccuracy of forging gears caused by the die elastic deformation