幂次为2和3的整变量非线性型的整数部分

用DavenportGHeilbronn方法证明了混合幂次为2,3,3的素变量非线性型的整数部分表示无穷多素数的问题:假设λ_(1),λ_(2),λ_(3)是非零实数,至少有一个λi/λj(1≤i<j≤3)为无理数,x1,x2,x3是正整数,那么λ_(1)x2^(1)+λ_(2)x3^(2)+λ_(3)x3^(3)的整数部分可表示无穷多素数.

Weekend and nighttime effect on the prognosis of peptic ulcer bleeding

AIM:To evaluate whether weekend or nighttime admission affects prognosis of peptic ulcer bleeding despite early endoscopy.METHODS:Retrospective data collection from four referral centers,all of which had a formal out-of-hours emergency endoscopy service,even at weekends.A total of 388 patients with bleeding peptic ulcers who were admitted via the emergency room between January 2007 and December 2009 were enrolled.Analyzed parameters included time from patients' arrival until endoscopy,mortality,rebleeding,need for surgery and length of hospital stay.RESULTS:The weekday and weekend admission groups comprised 326 and 62 patients,respectively.There were no significant differences in baseline characteristics between the two groups,except for younger age in the weekend group.Most patients (97%) had undergone early endoscopy,which resulted in a low mortality rate regardless of point of presentation (1.8% overall vs 1.6% on the weekend).The only outcome that was worse in the weekend group was a higher rate of rebleeding (12% vs 21%,P = 0.030).However,multivariate analysis revealed nighttime admission and a high Rockall score (≥ 6) as significant independent risk factors for rebleeding,rather than weekend admission.CONCLUSION:Early endoscopy for peptic ulcer bleeding can prevent the weekend effect,and nighttime admission was identified as a novel risk factor for rebleeding,namely the nighttime effect.

A topology optimization method based on element independent nodal density

A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.

素数k次方和的非线性型的整数部分

运用Dawmport-Heilbronn方法证明了:如果μ_1…,μ_r是不全为负的非零实数,至少一个μ_j(1≤j≤r)是无理数,k,m,r是正整数,k≥4,r≥2^(k-1)+1,则存在无穷多素数p_1,…,p_r,p,使得[μ_1p_1~k+…+μ_rp_r^k]=mp.特别地,[μ_1p_1~k+…+μ_rp_r^k]可表示无穷多素数.

Half-Lives for Alpha Radioactivity of Elements with 104 ≤Z≤120 within Unified Fission Model

α decay half-lives are calculated using the Qα values obtained by Semi-empirical Shell Model in the framework of the Unified Fission Model （UFM） with the Coulomb repulsion, nuclear attraction due to proximity potential, and rotational energy due to angular momentum transfer of a particle. In addition, the calculated and experimental half-lives of 425 nuclei are compared to check the validity of the model applied on α decay. The calculated half-lives of decay are in good agreement with the experimental data. Finally, some useful predications on the α decay half-lives are provided for future experiments.

幂次为2,3,4,5的素变量非线性型的整数部分

考虑了一个混合幂次为2，3，4，5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了：如果λ1，λ2，λ3，λ4是正实数，至少有一个λi/λj（1≤i〈 j≤4）是无理数，那么存在无穷多素数p1，p2，p3，p4，p，使得[λ1p12＋λ2p23＋λ3p34＋λ4p45]=p.

Determination of Natural Frequencies of Multilayered Plates by Mixed Finite Elements

Natural frequencies for multilayer plates are calculated by mixed finite element method. The main object of this paper is to use the mixed model for multilayer plates, analyzing each layer as an isolated plate, where the continuity of displacements is achieved by Lagrange multipliers （representing static variables）. This procedure allows us to work with any model for single plate （so as to ensure the proper behavior of each layer）, and the complexity of the multilayer system is avoided by ensuring the condition of displacements by the Lagrange multipliers （static variables）. The plate is discretized by finite element modeling based on a primary hybrid model, where the domain is divided by quadrilateral, both for the displacement field and static variables. This mixed element for plates was implemented and several examples of vibrations have been verified successfully by the results obtained by other methods in the literature.

Responses of Grassland Net Primary Productivity to Environmental Variables in Northern China

Various environmental factors affect net primary productivity （NPP） of grassland ecosystem. Extensive reports on the effects of environmental variables on NPP can be found in literature. However, the agreement on the relative importance of various factors in shaping the spatial pattern of grassland NPP has not yet been reached. Here a grassland in situ NPP database comprising 602 samples in northern China for 1980-1999 was developed based on a literature review of published biomass and forage yield field measurements. Correlation analyses and dominance analysis were used to quantify the separate and combined effects of environmental variables （climate topography and soil） on spatial variation in NPP separately. Grassland NPP ranged from 4.76 g C m-2a-1 to 975.94gCm-2a-1, showing significant variations in space. NPP increased with annual precipitation and declined with annual mean temperature significantly. Specifically, precipitation had the greatest impact on deserts, followed by steppes and meadows. Grassland NPP decreased with increasing altitude because of water limitation, and positively correlated with slope, but weakly correlated with aspect. Soil quality showed positive effects on NPP. Annual precipitation was the dominant factor affecting the spatial variability of net primary productivity, followed by elevation.