关键词： 高中数学   算法思想   应用探究  

摘要： 在科学技术迅猛发展的今天,信息技术和互联网技术被广泛应用于高中数学教学的领域中。无论是信息技术还是互联网技术,从本质上来讲核心思想核心内容都是算法,因此教师可从算法的角度来深入剖析高中数学教学。

关键词： 小学数学   比较思想   算法教学   应用   研究  

摘要： 小学生处在生长发育期,不可能在一夜之间形成较高的抽象思维能力与逻辑思维能力,在数学学习上存在着一定的难度。因此,教师应当认真研究小学生的思维方式,选择适合学生知识结构、认知特点、心理特征的比较形式,引导学生掌握比较思想,最终提高学生的数学素质。本文将研究如何在小学数学算法教学中应用比较思想。

关键词： Grobner-Shirshov basis   Poisson algebra   Word problem  

摘要： We develop a new theory of Grobner Shirshov bases for Poisson algebras, which requires to introduce several nontrivial new techniques. As applications, we solve the word problem for finitely presented Poisson algebras in the case of a single relation with a leading monomial of Lie type and in the case when enough relations involve the Poisson bracket of generators. (C) 2019 Elsevier Inc. All rights reserved.

关键词： 数学课堂   算法优化与多样化   个性发展  

摘要： 算法是数学的重要组成部分,也是数学学习的重难点之一,而在数学教学中进行算法教学的改革,虽然过程艰辛,但是益处颇多。算法改革的具体内容包括算法的多样化与优化两个层面,这对于促进学生的个性发展大有裨益,需要得到教师的鼓励和提倡。以下,笔者将结合自身教学的多年经验,就数学课上如何多样化与优化算法简要谈谈自己的看法与观点。

关键词： Ocean color remote sensing  

摘要： Two regional bio-optical algorithms are combined to retrieve the Chlorophyll-a (Chl-a) concentration in the Black Sea. The first is a band-ratio algorithm that computes Chl-a as a function of the slope of Remote Sensing Reflectance (R-RS) values at two wavelengths using a polynomial regression that captures the overall data trend, enhancing extrapolation results. The second algorithm is a Multilayer Perceptron neural net based on Rgs values at three individual wavelengths that features interpolation capabilities helpful to fit data non-linearities. A new merging scheme is then designed to benefit from the complementarity of the two approaches. Remote sensing data employed to demonstrate the merging of regional results for the Black Sea are those acquired by the Ocean and Land Color Instrument on board Sentinel-3A to acknowledge the need for data products of higher accuracy within the long-term Copernicus program.

关键词： OpenMP   task parallelism   linear algebra algorithms   NUMA   energy efficiency  

摘要： In this article, we analyze performance and energy consumption of five OpenMP runtime systems over a non-uniform memory access (NUMA) platform. We also selected three CPU-level optimizations or techniques to evaluate their impact on the runtime systems: processors features Turbo Boost and C-States, and CPU Dynamic Voltage and Frequency Scaling through Linux CPUFreq governors. We present an experimental study to characterize OpenMP runtime systems on the three main kernels in dense linear algebra algorithms (Cholesky, LU, and QR) in terms of performance and energy consumption. Our experimental results suggest that OpenMP runtime systems can be considered as a new energy leverage, and Turbo Boost, as well as C-States, impacted significantly performance and energy. CPUFreq governors had more impact with Turbo Boost disabled, since both optimizations reduced performance due to CPU thermal limits. An LU factorization with concurrent-write extension from libKOMP achieved up to 63% of performance gain and 29% of energy decrease over original PLASMA algorithm using GNU C compiler (GCC) libGOMP runtime.

关键词： Port industrial zone   Spatial layout   Multi-objective programming   Systematic layout planning   Simulated annealing algorithm  

摘要： The spatial layout of the port industrial zone problem is a core issue in port industrial zone planning, and it directly affects the actual effects of the port industrial zone. Firstly, considering that existing port industrial zone planning lacks in methods of quantitative analysis, this paper constructs a Mathematical model based on multi-objective programming, and the optimal scale of various industries of port industrial zone is obtained. Secondly, the paper takes the maximum dependence degree of port as objective function by using systematic layout planning tools, and solves the spatial layout of the port industrial zone. Finally, by taking Binhai Port industrial zone of China as an example, a port industrial zone spatial layout model is constructed and solved through simulated annealing algorithm. The optimal spatial layout program for Binhai Port industrial zone of China was obtained, which verifies the feasibility and accuracy of the model.

关键词： Quantum affine algebras   Quantum Grothendieck rings   Kazhdan-Lusztig algorithm   T-systems   Quantum cluster algebras   Dual canonical bases  

摘要： We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories C-2,C-Bn and C-Q,C-A2n-1 of finite-dimensional representations of quantum affine algebras of types Bn-(1) and A(2n-1)((1)), respectively. Our proof relies in part on the corresponding quantum cluster algebra structures. Moreover, we prove that our isomorphisms specialize at t = 1 to the isomorphisms of (classical) Grothendieck rings obtained recently by Kashiwara, Kim and Oh by other methods. As a consequence, we prove a conjecture formulated by the first author in 2002: the multiplicities of simple modules in standard modules in C-2,C-Bn are given by the specialization of certain analogues of Kazhdan-Lusztig polynomials and the coefficients of these polynomials are positive. (C) 2019 Elsevier Inc. All rights reserved.