《小问题》2019-1解答

问题:圆环半径为r,质量为m,以水平速度v0与水平地面接触。接触时,圆环与其移动速度v0在同一个铅锤平面内。试计算在何时何处圆环开始作纯滚动,在这过程中所受到的动能损失与动量损失,并说明这些损失的来由。

LOCAL BAGGING AND ITS APPLICATIONON FACE RECOGNITION

Bagging is not quite suitable for stable classifiers such as nearest neighbor classifiers due to the lack of diversity and it is difficult to be directly applied to face recognition as well due to the small sample size （SSS） property of face recognition. To solve the two problems,local Bagging （L-Bagging） is proposed to simultaneously make Bagging apply to both nearest neighbor classifiers and face recognition. The major difference between L-Bagging and Bagging is that L-Bagging performs the bootstrap sampling on each local region partitioned from the original face image rather than the whole face image. Since the dimensionality of local region is usually far less than the number of samples and the component classifiers are constructed just in different local regions,L-Bagging deals with SSS problem and generates more diverse component classifiers. Experimental results on four standard face image databases （AR,Yale,ORL and Yale B） indicate that the proposed L-Bagging method is effective and robust to illumination,occlusion and slight pose variation.

Ecological Environment Problems and Countermeasures of Small and Middle-sized Rivers in Shandong Province

Water uses in small and middle-sized rivers, and non-ecological treatment model has deteriorated local environment in Shandong. The research reviewed ecological environment status quo of small and middle rivers and concluded existing problems. Finally, ecological treatments were proposed based on treatments at home and abroad in order to improve eco-environment of rivers and build better Shandong.

浙江省与“一带一路”沿线国家贸易现状及发展思路研究

"一带一路"是中国特色社会主义新时代进一步深化开放的重大战略部署。浙江省现阶段处于工业化中后期,而"一带一路"沿线国家处于不同的工业化阶段,形成了不同的优势产业类型,浙江与"一带一路"沿线国家贸易潜力巨大。本文选取越南、印度尼西亚、泰国、沙特阿拉伯、伊朗、南非6个国家作为分析样本,采集杭州海关与上述国家进出口数据,进行产业内贸易指数计算,并对机电、纺织、化工三大重点行业国际贸易情况进行分析,最后对浙江与"一带一路"沿线国家外贸发展提出建议。总体发展思路是,针对"一带一路"沿线国家不同的产业梯度及其与浙江省产业不同的竞争状态,对于产业内贸易指数高的行业,应着重产品差别化,对产业内贸易指数较低、互补性强的行业,则应着眼于利用"一带一路"带来的战略机遇,大力拓展新兴国家市场。

Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization

Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.

Signal timing optimization model based on dual-ring phase scheme for roundabout

A signal optimization model for roundabout was control concept were used to eliminate the conflict points proposed based on dual-ring scheme and two stop lines for left turns and weaving sections at a roundabout. A cycle length minimization problem was considered to generate optimal signal timings for roundabout, and a set of constraints to ensure feasibility and safety of the resulting optimal signal settings were proposed. Extensive experimental analyses in comparison with signalized intersection reveal that the proposed model is quite promising for application in design of roundabout signals, and the minimum cycle length can decrease from 186 s to 79 s while the capacity increases from 8 682 pcu/h to 9 011 pcu/h under high demand scenario. Sensitivity analysis with respect to the system performance show that the lane assignment plan, number of circulatory lanes and left turn ratio are three critical factors which have dominate impacts on performance of signalized roundabout

A Preconditioned Fractional Tikhonov Regularization Method for Large Discrete Ill-posed Problems

The generalized Tikhonov regularization method is one of the most classical methods for the solution of linear systems of equations that arise from the discretization of linear ill-posed problems.However,the approximate solution obtained by the Tikhonov regularization method in general form may lack many details of the exact solution.Combining the fractional Tikhonov method with the preconditioned technique,and using the discrepancy principle for determining the regularization parameter,we present a preconditioned projected fractional Tikhonov regularization method for solving discrete ill-posed problems.Numerical experiments illustrate that the proposed algorithm has higher accuracy compared with the existing classical regularization methods.

Transceiver Optimization for Multi-Antenna Device-to-Device Communications

It has been shown that the deployment of device-to-device(D2D) communication in cellular systems can provide better support for local services. However, improper design of the hybrid system may cause severe interference between cellular and D2D links. In this paper, we consider transceiver design for the system employing multiple antennas to mitigate the interference. The precoder and decoder matrices are optimized in terms of sum mean squared error(MSE) and capacity, respectively. For the MSE minimization problem, we present an alternative transceiver optimization algorithm. While for the non-convex capacity maximization problem, we decompose the primal problem into a sequence of standard convex quadratic programs for efficient optimization. The evaluation of our proposed algorithms for performance enhancement of the entire D2D integrated cellular system is carried out through simulations.

A Discrete Artificial Bee Colony Algorithm for Minimizing the Total Flow Time in the Blocking Flow Shop Scheduling

A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion.

On the Minimum Spanning Tree Determined by n Points in the Unit Square

Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.

A Distributed User Association and Resource Allocation Method in Cache-Enabled Small Cell Networks

Cache-enabled small cell networks have been regarded as a promising approach for network operators to cope with the explosive data traffic growth in future 5 G networks. However, the user association and resource allocation mechanism has not been thoroughly studied under given content placement situation. In this paper, we formulate the joint optimization problem of user association and resource allocation as a mixed integer nonlinear programming(MINLP) problem aiming at deriving a balance between the total utility of data rates and the total data rates retrieved from caches. To solve this problem, we propose a distributed relaxing-rounding method. Simulation results demonstrate that the distributed relaxing-rounding method outperforms traditional max-SINR method and range-expansion method in terms of both total utility of data rates and total data rates retrieved from caches in practical scenarios. In addition, effects of storage and backhaul capacities on the performance are also studied.

Global optimization by small-world optimization algorithm based on social relationship network

A fast global convergence algorithm, small-world optimization (SWO), was designed to solve the global optimization problems, which was inspired from small-world theory and six degrees of separation principle in sociology. Firstly, the solution space was organized into a small-world network model based on social relationship network. Secondly, a simple search strategy was adopted to navigate into this network in order to realize the optimization. In SWO, the two operators for searching the short-range contacts and long-range contacts in small-world network were corresponding to the exploitation and exploration, which have been revealed as the common features in many intelligent algorithms. The proposed algorithm was validated via popular benchmark functions and engineering problems. And also the impacts of parameters were studied. The simulation results indicate that because of the small-world theory, it is suitable for heuristic methods to search targets efficiently in this constructed small-world network model. It is not easy for each test mail to fall into a local trap by shifting into two mapping spaces in order to accelerate the convergence speed. Compared with some classical algorithms, SWO is inherited with optimal features and outstanding in convergence speed. Thus, the algorithm can be considered as a good alternative to solve global optimization problems.

The Extremal Problem on Cartan-egg Domain of the First Type

In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.

Bottleneck Analysis of the Minimum Cost Problem for the Generalized Network Based on Augmented Forest Structure

The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented forest structure, then augments flows on the negative cost graphs until the optimal revolution is gained. Bottleneck structure is presented after analyzing the augmented forest structure. The negative cost augmented graphs are constructed with the bottleneck structure. The arcs that block the negative cost augmented graph are the elements of the bottleneck. The bottleneck analysis for the generalized circulation problem, the minimum circulation problem and the circulation problem are discussed respectively as the basal problems, then that for MCPGN is achieved. An example is presented at the end.

A heuristic method for solving triangle packing problem

Given a set of triangles and a rectangle container, the triangle packing problem is to determine if these triangles can be placed into the container without overlapping. Triangle packing problem is a special case of polygon packing problem and also NP-hard, so it is unlikely that an efficient and exact algorithm can be developed to solve this problem. In this paper, a new concept of rigid placement is proposed, based on which a discrete solution space called rigid solution space is constructed. Each solution in the rigid solution space can be built by continuously applying legal rigid placements one by one until all the triangles are placed into the rectangle container without overlapping. The proposed Least-Destruction-First (LDF) strategy determines which rigid placement has the privilege to go into the rectangle container. Based on this, a heuristic algorithm is proposed to solve the problem. Combining Least-Destruction-First strategy with backtracking, the corresponding backtracking algorithm is proposed. Computa- tional results show that our proposed algorithms are efficient and robust. With slight modification, these techniques can be con- veniently used for solving polygon packing problem.

Solving Three Types of Satellite Gravity Gradient Boundary Value Problems by Least-Squares

The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γ zz },{Γ xz , Γ yz} and {Γ xx -Γ yy ,2 Γxy}are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field.

Solving constrained minimax problem via nonsmooth equations method

A new nonsmooth equations model of constrained minimax problem was de-rived. The generalized Newton method was applied for solving this system of nonsmooth equations system. A new algorithm for solving constrained minimax problem was established. The local superlinear and quadratic convergences of the algorithm were discussed.

Six Sigma： The Panacea to Sustainability

Whilst there are a number of qualified methodologies, the researchers have opted to utilise the tools available through Six Sigma to prove that Six Sigma can be used to save resources and improve quality and process. Five industry sectors were identified as the ones to be surveyed using quantitative and qualitative methods and finally piloting the results on five different SMEs. Since this is a relative new methodology to the Cypriot entrepreneur and regrettably at the time of carrying out the study an international financial crisis caused a lot of financial problems to many respondents and as such could not see the immediate effects or benefits of Six Sigma and were reluctant to co-operate or participate. The Six Sigma methodology can be customized to industrial sectors and a tailored version of the methodology can be developed for a particular process or problem. The paper illustrates the problem areas identified from both the qualitative and quantitative research per industry. This is the first study carried out on Six Sigma in a small economy like Cyprus and tested on five industry sectors using both qualitative and quantitative methods

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.

Optimization Framework for Conceptual Powertrain Design

With an increasing number of vehicles with alternative powertrains, the choice of the most appropriate powertrain system for a vehicle class or a load cycle is challenging. This paper introduces a method to design an optimal alternative powertrain based on a longitudinal dynamic simulation. The objective function of the minimization problem describes the characteristic map of the traction system. The goal of the optimization is to minimize fuel consumption respectively energy demand. Different types of propulsion systems are investigated. The results show that the proposed method delivers useful alternative powertrains by applying an optimization with reasonable restrictions.