New algorithm for tensor contractions on multi‐core CPUs,GPUs, and accelerators enables CCSD and EOM‐CCSD calculations with over 1000 basis functions on a single compute node

A new hardware‐agnostic contraction algorithm for tensors of arbitrary symmetry and sparsity is presented. The algorithm is implemented as a stand‐alone open‐source code libxm . This code is also integrated with general tensor library libtensor and with the Q‐Chem quantum‐chemistry package. An overview of the algorithm, its implementation, and benchmarks are presented. Similarly to other tensor software, the algorithm exploits efficient matrix multiplication libraries and assumes that tensors are stored in a block‐tensor form. The distinguishing features of the algorithm are: (i) efficient repackaging of the individual blocks into large matrices and back, which affords efficient graphics processing unit (GPU)‐enabled calculations without modifications of higher‐level codes; (ii) fully asynchronous data transfer between disk storage and fast memory. The algorithm enables canonical all‐electron coupled‐cluster and equation‐of‐motion coupled‐cluster calculations with single and double substitutions (CCSD and EOM‐CCSD) with over 1000 basis functions on a single quad‐GPU machine. We show that the algorithm exhibits predicted theoretical scaling for canonical CCSD calculations, O (N ⁶), irrespective of the data size on disk. © 2017 Wiley Periodicals, Inc.     

等速上仰翼型动态失速现象研究

翼型大迎角绕流的静态失速将造成升力突降和气动性能急剧恶化，但利用非定常运动所产生 的动态失速效应，可以大大地延缓气流分离和失速现象的发生. 采用Rogers发 展的双时间步Roe格式，求解拟压缩性修正不可压N-S方程. 数值模拟了低雷诺数 ($Re=4.8 \times 10^{4}$)条件下NACA0015翼型作等速上仰($\alpha =0^{\circ} \sim 60^{\circ}$)的动态失速过程，同Walker的试验结果比 较，验证了计算结果的正确性. 研究了该过程中主涡、二次涡和三次涡的发展，升 力系数随攻角变化，以及不同上仰速度对动态失速效应所造成的影响.     

带有无界势和一般时间频率的非周期离散非线性Schr#246;dinger方程：无穷多个孤立子

本文研究下面的非周期离散非线性Schrödinger 方程：
-Δu_n + v_nu_n - ωun = g_n（u_n）,n ∈ Z,
其中V = {v_n}_n∈Z 和g_n 都是非周期的,当|n| → +∞ 时,v_n → +∞,并且时间频率ω ∈ R 可以满足下面的任何一种情形：（1）ω 属于算子-Δ + V 的一个有限谱间隔;（2）ω < inf σ（-Δ + V）;（3）ω ∈ σ（-Δ+ V）,其中σ（-Δ+ V）表示-Δ+ V的谱. 本文将用一些局部条件（在无穷远或零处）来代替一些全局条件. 利用变化的喷泉定理,当非线性项在无穷远处是超线性时,本文得到这个方程的无穷多个非平凡孤立子,并且,也得到指数衰减的孤立子的存在性.     

Global Parametric Sufficient Efficiency Conditions for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized （a,n,p）-V-Invex Functions

In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized (α, η, ρ)-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.     

Introduction of quantum finite-size effects in the Mie's theory for a multilayered metal sphere in the dipolar approximation: Application to free and matrix-embedded noble metal clusters

A mixed classical/quantum model for calculating the optical response of free and matrix-embedded multilayered metal spheres in the dipolar approximation is presented. The conduction electrons are quantum-mechanically treated in the framework of the time-dependent local-density-approximation formalism (TDLDA), whereas the surrounding matrix, the ionic metal backgrounds and the non-metallic materials are classically described through homogeneous charge distributions or/and dielectric media. Except for the TDLDA calculations, the present formalism is completely analytical and can be applied to coated spheres with any number of metal or dielectric layers. Contrary to the previous TDLDA-based models involving an inner or/and an outer dielectric medium (one or two interfaces), all the dielectric effects (screening and absorption) are self-consistently calculated. In particular, the interband transitions and the mutual interplay between the conduction and core electrons are self-consistently treated. The deficiencies of the previous models are analyzed, and the results are compared with the classical Mie's theory, over the entire spectral range. The building-up of the classical absorption spectrum, consisting of the surface plasmon resonance and the interband transitions, is clearly observed as the cluster size increases. Received 15 March 1999 and Received in final form 11 October 1999     

Efimov's Effect in a Model of Perturbation Theory of the Essential Spectrum

A model operator similar to the energy operator of a system with a nonconserved number of particles is studied. The essential spectrum of the operator is described, and under some natural conditions on the parameters it is shown that there are infinitely many eigenvalues lying below the bottom of the essential spectrum.     

Uncertainty relations for entangled states

A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should employ when doing any calculation using the entangled wave function of the pair. This new relation reduces to Heisenberg’s uncertainty relation when the particles have no correlation and suggests that we can have new lower bounds for the product of position and momentum dispersions.     

类p-Laplace方程的无穷多解的存在性

本文研究了类p-Laplace方程,利用证明其对应的变分泛函满足Cerami条件,得到了无穷多个大能量解的存在性,推广并改进了已有结果.     

灰色动态模型及其在人口预测中的应用

一个国家人口的数量直接影响着其经济、社会的发展和资源的利用 ,中国是世界上人口的第一大国 ,人口问题一直是制约中国发展的第一因素 .本文应用灰色系统等维灰数递补动态预测模型 ,对中国未来5 0年的人口数量进行了动态预测 ,通过检验表明 ,该模型合理、方法简便可行、结果符合实际 ,为中国经济和社会发展的决策和研究提供了科学依据