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1.
贺屹  蔡力勋  陈辉  彭云强 《力学学报》2018,50(3):579-588
表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.   相似文献   
2.
An equivalence is proven between the Riemann hypothesis and the speed of convergence to of the probability that two independent random variables following the same geometric distribution are coprime integers, when the parameter of the distribution goes to 0.  相似文献   
3.
This paper reviews some of the principal uses, over almost seven decades, of correlations, in both Eulerian and Lagrangian frames of reference, of properties of turbulent flows at variable spatial locations and variable time instants. Commonly called space—time correlations, they have been fundamental to theories and models of turbulence as well as for the analyses of experimental and direct numerical simulation turbulence data.  相似文献   
4.
Probability concepts and results are closely related to the study of zeros of the classical Riemann zeta function and its affinity to Gaussian and Gamma distributions. This is elaborated in obtaining the functional and integral equations for the zeta and in the determination first of the nonzero sets and then sets containing almost all (i.e., for the CLT probability measure) nontrivial zeros of the zeta function ζ(·). Also probability distributions determined by the zeta, based on the behavior of their finite dimensional distributions of the ζ(σ +it), σ > 0; as t varies and particularly the results of Denjoy, slightly sharpened, and also one of Salem are included. Several related opinions and comments are discussed.  相似文献   
5.
We present measurements of Eulerian longitudinal velocity autocorrelations in homogeneous, isotropic, high-intensity (~9%) free-stream turbulence behind an active grid. Spatial correlations are measured using particle image velocimetry as well as with two-point hot-wire anemometry (HWA), while temporal correlations are measured using HWA. The temporal correlations are transformed into spatial correlations by using Taylor's ‘frozen’ hypothesis with both the mean as well as instantaneous velocities. A model relating Eulerian spatial and temporal autocorrelations is also used for this purpose. The differences from the measured spatial correlation resulting from the use of Taylor's hypothesis on the temporal correlation is quantified; even at this moderately high level of turbulent intensity, the result from the use of the instantaneous velocity as convection velocity is practically indistinguishable from that obtained using the mean velocity. Use of the model produces a good agreement between the estimates of the spatial correlation function. A relation between Eulerian spatial and temporal integral scales is also derived.  相似文献   
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7.
本文提出了结合平均小波系数法和自回归原始自助法的稳健长记忆检验,蒙特卡罗模拟显示该方法对于短期记忆过程具有稳定性。基于该方法对2005年4月8日至2015年6月30日的中国、美国、香港和德国股市进行了实证分析。全局检验结果表明仅中国的股票市场存在显著的长记忆,并且风险因素无法对长记忆解释,而美国、德国和香港的股市不存在长记忆。基于递增窗口的动态Hurst指数分析显示,金融危机时期4个股市都存在显著的长记忆。2010年后,除中国股市外,其余三个股市几乎不存在长记忆现象。  相似文献   
8.
We provide new semilocal convergence results for Newton-like method involving outer or generalized inverses in a Banach space setting. Using our new idea of recurrent functions and the same or weaker conditions than before [5-19 A. Ben-Israel and N.E. Greville ( 1974 ). Generalized Inverses: Theory and Applications, Pure and Applied Mathematics . Wiley-Interscience , New York . X. Chen and T. Yamamoto ( 1989 ). Convergence domains of certain iterative methods for solving nonlinear equations . Numer. Funct. Anal. Optimiz. 10 : 3748 . J.E. Dennis , Jr. ( 1968 ). On Newton-like methods . Numer. Math. 11 : 324330 . P. Deuflhard and C. Heindl ( 1979 ). Convergence theorems for Newton's method and extensions to related methods . SIAM J. Numer. Anal. 16 : 110 . J.M. Gutiérrez ( 1997 ). A new semilocal convergence theorem for Newton's method . J. Comp. Appl. Math. 79 : 131145 . J.M. Gutiérrez , M.A. Hernández , and M.A. Salanova ( 1995 ). Accessibility of solutions by Newton's method . Internat. J. Comput. Math. 57 : 239247 . W.M. Häubler ( 1986 ). A Kantorovich-type convergence analysis for the Gauss–Newton methods . Numer. Math. 48 : 119125 . L.V. Kantorovich and G.P. Akilov ( 1964 ). Functional Analysis . Pergamon Press , Oxford . M.Z. Nashed and X. Chen ( 1993 ). Convergence of Newton-like methods for singular operator equations using outer inverses . Numer. Math. 66 : 235257 . F.A. Potra and V. Ptàk ( 1980 ). Sharp error bounds for Newton's process . Numer. Math. 34 : 6772 . W.C. Rheinboldt ( 1968 ). A unified convergence theory for a class of iterative processes . SIAM J. Numer. Anal. 5 : 4263 . W.C. Rheinboldt ( 1977 ). An adaptive continuation process for solving systems of nonlinear equations . Polish Academy of Sciences, Banach Ctr. Publ. 3 : 129142 . T. Yamamoto ( 1987 ). A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions . Numer. Math. 49 : 203230 . T. Yamamoto ( 1987 ). A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. 51 : 545557 . T. Yamamoto ( 1989 ). Uniqueness of the solution in a Kantorovich-type theorem of Haubler for the Gauss–Newton method . Japan J. Appl. Math. 6 : 7781 . ], we provide more precise information on the location of the solution and finer bounds on the distances involved. Moreover, since our Newton–Kantorovich-type hypothesis is weaker than before, we can now cover cases not previously possible.

Applications and numerical examples involving a nonlinear integral equation of Chandrasekhar-type and a differential equation with Green's function are also provided in this study.  相似文献   
9.
We show that every compact space of large enough size has a realcompact subspace of size κ, for κ?c. We also show that an uncountable realcompact space whose pseudocharacter is at most ω1, has a realcompact subspaces of size ω1, thus, by continuum hypothesis, every uncountable realcompact space has realcompact subspace of size ω1.  相似文献   
10.
Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.  相似文献   
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