转换思维 关注生成 让数学更具生命力

一年一度的"把握学科特点构建高效课堂"青年教师课堂大比武活动正式拉开帷幕。青年教师纷纷潜心钻研教材,关注学生已有的认知基础,精心设计适合学生特点的教学流程,反复推敲锤炼课堂教学语言,制作精美的直观的教学课件,在课堂中生成的精彩瞬间让人回味无穷。本文将从四个方面阐述青年教师为打造高效课堂而做出的努力。

An Efficient Algorithm for Query Transformation in Semantic Query Optimization

Semantic query optimization (SQO) is comparatively a recent approach for the transformation of given query into equivalent alternative query using matching rules in order to select an optimal query based on the costs of executing alternative queries. The key aspect of the algorithm proposed here is that previous proposed SQO techniques can be considered equally in the uniform cost model, with which optimization opportunities will not be missed. At the same time, the authors used the implication closure to guarantee that any matched rule will not be lost. The authors implemented their algorithm for the optimization of decomposed sub-query in local database in Multi-Database Integrator (MDBI), which is a multidatabase project. The experimental results verify that this algorithm is effective in the process of SQO.

Cryptanalysis of a Cryptosystem with Non- Commutative Platform Groups

A cryptosystem with non-commutative platform groups based on conjugator search problem was recently introduced at Neural Computing and Applications 2016. Its versatility was illustrated by building a public-key encryption scheme. We propose an algebraic key-recovery attack in the polynomial computational complexity. Furthermore, we peel off the encryption and decryption process and propose attack methods for solving the conjugator search problem over the given non-abelian group. Finally, we provide corresponding practical attack examples to illustrate the attack methods in our cryptanalysis, and provide some improved suggestions.

Direction of Arrivals Estimation for Correlated Broadband Radio Signals by MVDR Algorithm Using Wavelet

A theoretical relationship between the wavelet transform and the fast fourier transformation(FFT) methods in broadband wireless signal is proposed for solving the direction of arrivals(DOAs) estimation problem. This leads naturally to the derivation of minimum variance distortionless response(MVDR) algorithm, which combines the benefits of subspace methods with those of wavelet, and spatially smoothed versions are utilized which exhibits good performance against correlated signals. We test the method's performance by simulating and comparing the performance of proposed algorithm, FFT MVDR and MVDR with correlated signals, and an improved performance is obtained.

A Vehicle Routing Problem Based on Intelligent Batteries Transfer Management for the EV Network

Batteries transfer management is one important aspect in electric vehicle(EV)network's intelligent operation management system.Batteries transfer is a special and much more complex VRP(Vehicle Routing Problem) which takes the multiple constraints such as dynamic multi-depots,time windows,simultaneous pickups and deliveries,distance minimization,etc.into account.We call it VRPEVB(VRP with EV Batteries).This paper,based on the intelligent management model of EV's battery power,puts forward a battery transfer algorithm for the EV network which considers the traffic congestion that changes dynamically and uses improved Ant Colony Optimization.By setting a reasonable tabv range,special update rules of the pheromone and path list memory functions,the algorithm can have a better convergence,and its feasibility is proved by the experiment in an EV's demonstration operation system.

Inverse Problem and Variation Method to Optimize Cascade Heat Exchange Network in Central Heating System

Urban heating in northern China accounts for 40% of total building energy usage. In central heating systems, heat is often transferred from heat source to users by the heat network where several heat exchangers are installed at heat source, substations and terminals respectively. For given overall heating capacity and heat source tempera- tore, increasing the terminal fluid temperature is an effective way to improve the thermal performance of such cascade heat exchange network for energy saving. In this paper, the mathematical optimization model of the cas- cade heat exchange network with three-stage heat exchangers in series is established. Aim at maximizing the cold fluid temperature for given hot fluid temperature and overall heating capacity, the optimal heat exchange area dis- tribution and the medium fluids＇ flow rates arc determined through inverse problem and variation method. The preliminary results show that the heat exchange areas should be distributed equally for each heat exchanger. It al- so indicates that in order to improve the thermal performance of the whole system, more heat exchange areas should be allocated to the heat exchanger whore flow rate difference between two fluids is relatively small. This work is important for guiding the optimization design of practical cascade heating systems.

Development of DNA computing and information processing based on DNA-strand displacement

DNA computing, currently a hot research field in information processing, has the advantages of parallelism, low energy consumption, and high storability, therefore, it has been applied to a variety of complicated computational problems. The emerging field of DNA nanotechnology has also developed quickly; within it, the method of DNA strand displacement has drawn great attention because it is self-induced, sensitive, accurate, and operationally simple. This article summarizes five aspects of the recent developments of DNA-strand displacement in DNA computing:(1) cascading circuits;(2) catalyzed reaction;(3) logic computation;(4) DNA computing on surfaces; and(5) logic computing based on nanoparticles guided by strand displacement. The applications and mechanisms of strand displacement in DNA computing are discussed and possible future developments are presented.

Localized collocation schemes and their applications

This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.

Dynamic conducting crack propagation in piezoelectric materials:Mode-II problem

This paper studies the dynamic conducting crack propagation in piezoelectric solids under suddenly in-plane shear loading. Based on the integral transform methods and the Wiener-Hopf technique, the resulting mixed boundary value problem is solved. The analytical solutions of the dynamic stress intensity factor and dynamic electric displacement intensity factor for the Mode II case are derived. Furthermore, the numerical results are presented to illustrate the characteristics of the dynamic crack propagation. It is shown that the universal functions for the dynamic stress and electric displacement intensity factors vanish if the crack propagation speed equals the generalized Rayleigh speed. The results indicate that the defined electro-mechanical coupling coefficient is of great importance to the universal functions and stress intensity factor history.

Integral Transform Methods for Inverse Problem of Heat Conduction with Known Boundary of a Thin Rectangular Object and its Stresses

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D： -a〈xSa; -b〈_y〈b; 0〈z〈h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.