Abstract:
Flexible rolling is a forming process based on thickness reduction, and the precision of thickness reduction is the key factor affecting bending deformation. The major purpose of the present work is to solve the problem of bending deformation error caused by insufficient thickness reduction. Under the condition of different rolling reductions with the same sheet thickness and the same thickness reduction with different sheet thicknesses, the thickness reduction error of sheet metal is analyzed. In addition, the bending deformation of sheet metal under the same conditions is discussed and the influence of the multi-step forming process on the thickness reduction error is studied. The results show that, under the condition of the same sheet thickness, the thickness reduction error increases with increasing rolling reduction because of an increase in work hardening. As rolling reduction increases, the longitudinal bending deformation decreases because of the decrease of the maximum thickness difference. Under the condition with the same thickness reduction, the thickness reduction error increases because of the decrease of the rolling force with increasing sheet thickness. As the sheet thickness increases, the longitudinal bending deformation increases because of the increase in the maximum thickness difference. A larger bending deformation is divided into a number of small bending deformations in a multi-step forming process, avoiding a sharp increase in the degree of work hardening; the thickness reduction error is effectively reduced in the multi-step forming process. Numerical simulation results agree with the results of the forming experiments.

Abstract:
AIM: To demonstrate the oncologic outcomes of low rectal cancer and to clarify the risk factors for survival, focusing particularly on the type of surgery performed. METHODS: Data from patients with low rectal carcinomas who underwent surgery, either sphincter-preserving surgery (SPS) or abdominoperineal resection (APR), at The First Affiliated Hospital of Sun Yat-sen University in China from August 1994 to December 2005 were retrospectively analyzed. RESULTS: Of 331 patients with low rectal cancer, 159 (48.0%) were treated with SPS. A higher incidence of positive resection margins and a higher 5-year cumulative local recurrence rate (14.7% vs 6.8%, P = 0.041) were observed in patients after APR compared to SPS. The five-year overall survival (OS) was 54.6% after APR and 66.8% after SPS (P = 0.018), and the 5-year disease-free survival (DFS) was 52.9% after APR and 65.5% after SPS (P = 0.013). In multivariate analysis, poor OS and DFS were significantly related to positive resection margins, pT3-4, and pTNM III-IV but not to the type of surgery. CONCLUSION: Despite a higher rate of positive resection margins after APR, the type of surgery was not identified as an independent risk factor for survival.

Abstract:
Standing sausage modes in flare loops are important for interpreting quasi-periodic pulsations (QPPs) in solar flare lightcurves. We propose an inversion scheme that consistently uses their periods $P$ and damping times $\tau$ to diagnose flare loop parameters. We derive a generic dispersion relation governing linear sausage waves in pressure-less straight tubes, for which the transverse density inhomogeneity takes place in a layer of arbitrary width $l$ and is of arbitrary form. We find that $P$ and $\tau$ depend on the combination of $[R/v_{\rm Ai}, L/R, l/R, \rho_{\rm i}/\rho_{\rm e}]$, where $R$ is the loop radius, $L$ is the looplength, $v_{\rm Ai}$ is the internal Alfv\'en speed, and $\rho_{\rm i}/\rho_{\rm e}$ is the density contrast. For all the density profiles examined, $P$ and $\tau$ experience saturation when $L/R \gg 1$, yielding an inversion curve in the $[R/v_{\rm Ai}, l/R, \rho_{\rm i}/\rho_{\rm e}]$ space with a specific density profile when $L/R$ is sufficiently large. When applied to a spatially unresolved QPP event, the scheme yields that $R/v_{\rm Ai}$ is the best constrained, whereas $l/R$ corresponds to the other extreme. For spatially resolved QPPs, while $L/R \gg 1$ cannot be assumed beforehand, an inversion curve remains possible due to additional geometrical constraints. When a spatially resolved QPP event involves another mode, as is the case for a recent event, the full set of $[v_{\rm Ai}, l, \rho_{\rm i}/\rho_{\rm e}]$ can be inferred. We conclude that the proposed scheme provides a useful tool for magneto-seismologically exploiting QPPs.

Abstract:
Standing fast sausage modes in flare loops were suggested to account for a considerable number of quasi-periodic pulsations (QPPs) in the light curves of solar flares. This study continues our investigation into the possibility to invert the measured periods $P$ and damping times $\tau$ of sausage modes to deduce the transverse Alfv\'en time $R/v_{\rm Ai}$, density contrast $\rho_{\rm i}/\rho_{\rm e}$, and the steepness of the density distribution transverse to flare loops. A generic dispersion relation (DR) governing linear sausage modes is derived for pressureless cylinders where density inhomogeneity of arbitrary form takes place within the cylinder. We show that in general the inversion problem is under-determined for QPP events where only a single sausage mode exists, be the measurements spatially resolved or unresolved. While $R/v_{\rm Ai}$ can be inferred to some extent, the range of possible steepness parameters may be too broad to be useful. However, for spatially resolved measurements where an additional mode is present, it is possible to deduce self-consistently $\rho_{\rm i}/\rho_{\rm e}$, the profile steepness, and the internal Alfv\'en speed $v_{\rm Ai}$. We show that at least for a recent QPP event that involves a fundamental kink mode in addition to a sausage one, flare loop parameters are well constrained, even if the specific form of the transverse density distribution remains unknown. We conclude that spatially resolved, multi-mode QPP measurements need to be pursued for inferring flare loop parameters.

Abstract:
Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere. We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field. Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued longitudinal wavenumber $k$ at given real angular frequencies $\omega$. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of $\omega_{\rm c}$, the critical angular frequency separating trapped from leaky waves. In contrast to the standing case, propagating sausage waves are allowed for $\omega$ much lower than $\omega_{\rm c}$. However, while able to direct their energy upwards, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for $\omega \lesssim 1.5 v_{\rm Ai}/a$, where $a$ and $v_{\rm Ai}$ are the cylinder radius and the Alfv\'en speed in the cylinder, respectively. We conclude that if a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.

Abstract:
In the areas of computer vision and CAD/CAM, it is often needed to represent an image or a 3D surface from discrete measured data. A novel algorithm for the shape representation and image reconstruction is presented in this paper, which integrates the theories of optimal approximation and data smoothing. A positive definite functional is set up according to Lagrange multiplier method, and solved by finite element method and Newton iteration method. The shape or image is then constructed on the basis of finite element interpolation. This algorithm combines the smoothing processing technique with finite element method, the influence of the noise in input data is eliminated and reconstructing precision is improved. The formulations to calculate Lagrange multiplier and the relevant equations of eight-node isoparametric finite element were dervied. Effects of the variations in smoothing factor, in the finite element mesh and in the amount of imput data on the reconstructed results were investigated. A Gauss surface and two images of sphere and saddle surface were represented from discrete data with imposed noise, the results show the effectiveness of presented method. To illustrate the applicability of the method, a Morie fringes image of a tensile composite plate containing a hole was reconstructed. The method is conceptually simple and relatively easy and expedient to apply. The number of input data required in the presented method is less than that in numerical interpolation and fitting and the method can be used to the problem of irregular region with coved boundary.

Abstract:
A finite element method to reconstruct 3D surface from the scattered data is presented in the paper. Based on the theories of optimal approximation and data smoothing, a positive definite functional is constructed and minimized by using the finite element best-fitting technique, then the optimal solution is obtained and the 3D surface is reconstruct by eight-node isoparametric finite element interpolation. The influence of noise in input data is eliminated effectively by the smoothing-finite element method. The number of input data required in the presented method is less than that in finite element fitting. The surface reconstructed is of high approximating precision and good smoothness. Numerical results show that this method is simple and expedient to use.

Abstract:
We examine the influence of a continuous density structuring transverse to coronal slabs on the dispersive properties of fundamental standing kink and sausage modes supported therein. We derive generic dispersion relations (DRs) governing linear fast waves in pressureless straight slabs with general transverse density distributions, and focus on the cases where the density inhomogeneity takes place in a layer of arbitrary width and in arbitrary form. The physical relevance of the solutions to the DRs is demonstrated by the corresponding time-dependent computations. For all profiles examined, the lowest-order kink modes are trapped regardless of longitudinal wavenumber $k$. A continuous density distribution introduces a difference to their periods of $\lesssim 13\%$ when $k$ is the observed range, relative to the case where the density profile takes a step-function form. Sausage modes and other branches of kink modes are leaky at small $k$, and their periods and damping times are heavily influenced by how the transverse density profile is prescribed, the lengthscale in particular. These modes have sufficiently high quality to be observable only for physical parameters representative of flare loops. We conclude that while the simpler DR pertinent to a step-function profile can be used for the lowest-order kink modes, the detailed information on the transverse density structuring needs to be incorporated into studies of sausage modes and higher-order kink modes.

Abstract:
Ultracompact dark matter minihalos (UCMHs) would be formed during the earlier universe if there were large density perturbations. If the dark matter can decay into the standard model particles, such as neutrinos, these objects would become the potential astrophysical sources and could be detected by the related instruments, such as IceCube. In this paper, we investigate the neutrino signals from the nearby UCMHs due to the gravitino dark matter decay and compare these signals with the background neutrino flux which is mainly from the atmosphere to get the constraints on the abundance of UCMHs.

Abstract:
This paper presents a classification of generic 6-revolute jointed (6R) manipulators using homotopy class of their critical point manifold. A part of classification is listed in this paper because of the complexity of homotopy class of 4-torus. The results of this classification will serve future research of the classification and topological properties of maniplators joint space and workspace.